JEE Advanced 2016 Paper 2 Offline
Paper was held on
Sun, May 22, 2016 2:00 AM
Chemistry
1
Extraction of copper from copper pyrite (CuFeS2) involves
2
For the following electrochemical cell at 298 K
Pt(s) | H2 (g, 1 bar) | H+ (aq, 1 M) || M4+ (aq), M2+ (aq) | Pt (s)
Ecell = 0.092 V when $${{\left[ {{M^{2 + }}(aq)} \right]} \over {\left[ {{M^{4 + }}(aq)} \right]}}$$ = 10x
Give, $$E_{{M^{4+}}/{M^{2 + }}}^o$$ = 0.151 V; 2.303 RT/F = 0.059 V
Pt(s) | H2 (g, 1 bar) | H+ (aq, 1 M) || M4+ (aq), M2+ (aq) | Pt (s)
Ecell = 0.092 V when $${{\left[ {{M^{2 + }}(aq)} \right]} \over {\left[ {{M^{4 + }}(aq)} \right]}}$$ = 10x
Give, $$E_{{M^{4+}}/{M^{2 + }}}^o$$ = 0.151 V; 2.303 RT/F = 0.059 V
The value of x is
3
Mixture (s) showing positive deviation from Raoult’s law at 35oC is (are)
4
The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are) :
5
Paragraph
Thermal decomposition of gaseous X2 to gaseous X at 298 K takes place according to the following equations:
X2 (g) $$\leftrightharpoons$$ 2X (g)
The standard reaction Gibbs energy, $$\Delta _rG^o$$, of this reaction is positive. At the start of the reaction, there is one mole of X2 and no X. As the reaction proceeds, the number of moles of X formed is given by $$\beta$$. Thus, $$\beta _{equilibrium}$$ is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given R = 0.083 L bar K-1 mol-1)
Question
The INCORRECT statement among the following for this reaction, is
Thermal decomposition of gaseous X2 to gaseous X at 298 K takes place according to the following equations:
X2 (g) $$\leftrightharpoons$$ 2X (g)
The standard reaction Gibbs energy, $$\Delta _rG^o$$, of this reaction is positive. At the start of the reaction, there is one mole of X2 and no X. As the reaction proceeds, the number of moles of X formed is given by $$\beta$$. Thus, $$\beta _{equilibrium}$$ is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given R = 0.083 L bar K-1 mol-1)
Question
The INCORRECT statement among the following for this reaction, is
6
Paragraph
Thermal decomposition of gaseous X2 to gaseous X at 298 K takes place according to the following equations:
X2 (g) $$\leftrightharpoons$$ 2X (g)
The standard reaction Gibbs energy, $$\Delta _rG^o$$, of this reaction is positive. At the start of the reaction, there is one mole of X2 and no X. As the reaction proceeds, the number of moles of X formed is given by $$\beta$$. Thus, $$\beta _{equilibrium}$$ is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given R = 0.083 L bar K-1 mol-1)
Question
The equilibrium constant Kp for this reaction at 298 K, in terms of $$\beta _{equilibrium}$$, is
Thermal decomposition of gaseous X2 to gaseous X at 298 K takes place according to the following equations:
X2 (g) $$\leftrightharpoons$$ 2X (g)
The standard reaction Gibbs energy, $$\Delta _rG^o$$, of this reaction is positive. At the start of the reaction, there is one mole of X2 and no X. As the reaction proceeds, the number of moles of X formed is given by $$\beta$$. Thus, $$\beta _{equilibrium}$$ is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given R = 0.083 L bar K-1 mol-1)
Question
The equilibrium constant Kp for this reaction at 298 K, in terms of $$\beta _{equilibrium}$$, is
7
According to Molecular Orbital Theory, which of the following statements is(are) correct?
8
The geometries of the ammonia complexes of Ni2+, Pt2+ and Zn2+, respectively, are
9
The correct order of acidity for the following compounds is
10
The major product of the following reaction sequence is:
11
In the following reaction, sequence in aqueous solution, the species X, Y and Z, respectively, are
$${S_2}O_3^{2 - }\buildrel {A{g^ + }} \over \longrightarrow \mathop X\limits_{Clear\,solution} \buildrel {A{g^ + }} \over \longrightarrow \mathop Y\limits_{White\,precipitate} \buildrel {With\,time} \over \longrightarrow \mathop Z\limits_{Black\,precipitate} $$
12
The qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of KCl, CH3OH and CH3(CH2)11 OSO$$_3^ - $$ Na+ at room temperature. The correct assignment of the sketches is
13
For "invert sugar", the correct statement(s) is(are)
(Given : specific rotations of (+)-sucrose, (+)-maltose, L-($$-$$)-glucose and L-(+)-fructose in aqueous solution are +66$$^\circ$$, +140$$^\circ$$, $$-$$52$$^\circ$$ and +92$$^\circ$$, respectively.)
14
Among the following reaction(s), which gives(give) tert-butyl benzene as the major product is(are)
15
Reagent(s) which can be used to bring about the following transformation is(are)
16
The nitrogen containing compound produced in the reaction of HNO3 with P4O10
17
The compound R is
18
The compound T is
Mathematics
1
Let $$a,\,b \in R\,and\,{a^{2\,}} + {b^2} \ne 0$$. Suppose
$$S = \left\{ {Z \in C:Z = {1 \over {a + ibt}}, + \in R,t \ne 0} \right\}$$, where $$i = \sqrt { - 1} $$. Ifz = x + iy and z $$ \in $$ S, then (x, y) lies on
$$S = \left\{ {Z \in C:Z = {1 \over {a + ibt}}, + \in R,t \ne 0} \right\}$$, where $$i = \sqrt { - 1} $$. Ifz = x + iy and z $$ \in $$ S, then (x, y) lies on
2
The value of
$$\sum\limits_{k = 1}^{13} {{1 \over {\sin \left( {{\pi \over 4} + {{\left( {k - 1} \right)\pi } \over 6}} \right)\sin \left( {{\pi \over 4} + {{k\pi } \over 6}} \right)}}} $$ is equal to
$$\sum\limits_{k = 1}^{13} {{1 \over {\sin \left( {{\pi \over 4} + {{\left( {k - 1} \right)\pi } \over 6}} \right)\sin \left( {{\pi \over 4} + {{k\pi } \over 6}} \right)}}} $$ is equal to
3
Let $$\widehat u = {u_1} \widehat i + {u_2}\widehat j + {u_3}\widehat k$$ be a unit vector in $${{R^3}}$$ and
$$\widehat w = {1 \over {\sqrt 6 }}\left( {\widehat i + \widehat j + 2\widehat k} \right).$$ Given that there exists a vector $${\overrightarrow v }$$ in $${{R^3}}$$ such that $$\left| {\widehat u \times \overrightarrow v } \right| = 1$$ and $$\widehat w.\left( {\widehat u \times \overrightarrow v } \right) = 1.$$ Which of the following statement(s) is (are) correct?
$$\widehat w = {1 \over {\sqrt 6 }}\left( {\widehat i + \widehat j + 2\widehat k} \right).$$ Given that there exists a vector $${\overrightarrow v }$$ in $${{R^3}}$$ such that $$\left| {\widehat u \times \overrightarrow v } \right| = 1$$ and $$\widehat w.\left( {\widehat u \times \overrightarrow v } \right) = 1.$$ Which of the following statement(s) is (are) correct?
4
Let $$P$$ be the image of the point $$(3,1,7)$$ with respect to the plane $$x-y+z=3.$$ Then the equation of the plane passing through $$P$$ and containing the straight line $${x \over 1} = {y \over 2} = {z \over 1}$$ is
5
Football teams $${T_1}$$ and $${T_2}$$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $${T_1}$$ winning, drawing and losing a game against $${T_2}$$ are $${1 \over 2},{1 \over 6}$$ and $${1 \over 3}$$ respectively. Each team gets $$3$$ points for a win, $$1$$ point for a draw and $$0$$ point for a loss in a game. Let $$X$$ and $$Y$$ denote the total points scored by teams $${T_1}$$ and $${T_2}$$ respectively after two games.
$$P\,\left( {X = Y} \right)$$ is
6
Football teams $${T_1}$$ and $${T_2}$$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $${T_1}$$ winning, drawing and losing a game against $${T_2}$$ are $${1 \over 2},{1 \over 6}$$ and $${1 \over 3}$$ respectively. Each team gets $$3$$ points for a win, $$1$$ point for a draw and $$0$$ point for a loss in a game. Let $$X$$ and $$Y$$ denote the total points scored by teams $${T_1}$$ and $${T_2}$$ respectively after two games.
$$\,\,\,\,P\,\left( {X > Y} \right)$$ is
7
Let
$$f\left( x \right) = \mathop {\lim }\limits_{n \to \infty } {\left( {{{{n^n}\left( {x + n} \right)\left( {x + {n \over 2}} \right)...\left( {x + {n \over n}} \right)} \over {n!\left( {{x^2} + {n^2}} \right)\left( {{x^2} + {{{n^2}} \over 4}} \right)....\left( {{x^2} + {{{n^2}} \over {{n^2}}}} \right)}}} \right)^{{x \over n}}},$$ for
all $$x>0.$$ Then
$$f\left( x \right) = \mathop {\lim }\limits_{n \to \infty } {\left( {{{{n^n}\left( {x + n} \right)\left( {x + {n \over 2}} \right)...\left( {x + {n \over n}} \right)} \over {n!\left( {{x^2} + {n^2}} \right)\left( {{x^2} + {{{n^2}} \over 4}} \right)....\left( {{x^2} + {{{n^2}} \over {{n^2}}}} \right)}}} \right)^{{x \over n}}},$$ for
all $$x>0.$$ Then
8
Area of the region
$$\left\{ {\left( {x,y} \right) \in {R^2}:y \ge \sqrt {\left| {x + 3} \right|} ,5y \le x + 9 \le 15} \right\}$$
is equal to
$$\left\{ {\left( {x,y} \right) \in {R^2}:y \ge \sqrt {\left| {x + 3} \right|} ,5y \le x + 9 \le 15} \right\}$$
is equal to
9
The value of $$\int\limits_{-{\pi \over 2}}^{{\pi \over 2}} {{{{x^2}\cos x} \over {1 + {e^x}}}dx} $$ is equal to
10
Let f: R $$ \to \left( {0,\infty } \right)$$ and g : R $$ \to $$ R be twice differentiable functions such that f'' and g'' are continuous functions on R. Suppose f'$$(2)$$ $$=$$ g$$(2)=0$$, f''$$(2)$$$$ \ne 0$$ and g'$$(2)$$ $$ \ne 0$$. If
$$\mathop {\lim }\limits_{x \to 2} {{f\left( x \right)g\left( x \right)} \over {f'\left( x \right)g'\left( x \right)}} = 1,$$ then
$$\mathop {\lim }\limits_{x \to 2} {{f\left( x \right)g\left( x \right)} \over {f'\left( x \right)g'\left( x \right)}} = 1,$$ then
11
Let $${F_1}\left( {{x_1},0} \right)$$ and $${F_2}\left( {{x_2},0} \right)$$ for $${{x_1} < 0}$$ and $${{x_2} > 0}$$, be the foci of the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 8} = 1$$. Suppose a parabola having vertex at the origin and focus at $${F_2}$$ intersects the ellipse at point $$M$$ in the first quadrant and at point $$N$$ in the fourth quadrant.
The orthocentre of the triangle $${F_1}MN$$ is
12
Let $${F_1}\left( {{x_1},0} \right)$$ and $${F_2}\left( {{x_2},0} \right)$$ for $${{x_1} < 0}$$ and $${{x_2} > 0}$$, be the foci of the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 8} = 1$$. Suppose a parabola having vertex at the origin and focus at $${F_2}$$ intersects the ellipse at point $$M$$ in the first quadrant and at point $$N$$ in the fourth quadrant.
If the tangents to the ellipse at $$M$$ and $$N$$ meet at $$R$$ and the normal to the parabola at $$M$$ meets the $$x$$-axis at $$Q$$, then the ratio of area of the triangle $$MQR$$ to area of the quadrilateral $$M{F_1}N{F_2}$$is
13
Let $$P$$ be the point on the parabola $${y^2} = 4x$$ which is at the shortest distance from the center $$S$$ of the circle $${x^2} + {y^2} - 4x - 16y + 64 = 0$$. Let $$Q$$ be the point on the circle dividing the line segment $$SP$$ internally. Then
14
Let $$P = \left[ {\matrix{ 1 & 0 & 0 \cr 4 & 1 & 0 \cr {16} & 4 & 1 \cr } } \right]$$ and I be the identity matrix of order 3. If $$Q = [{q_{ij}}]$$ is a matrix such that $${P^{50}} - Q = I$$ and $${{{q_{31}} + {q_{32}}} \over {{q_{21}}}}$$ equals
15
Let bi > 1 for I = 1, 2, ......, 101. Suppose logeb1, logeb2, ......., logeb101 are in Arithmetic Progression (A.P.) with the common difference loge2. Suppose a1, a2, ......, a101 are in A.P. such that a1 = b1 and a51 = b51. If t = b1 + b2 + .... + b51 and s = a1 + a2 + ..... + a51, then
16
Let a, b $$\in$$ R and f : R $$\to$$ R be defined by $$f(x) = a\cos (|{x^3} - x|) + b|x|\sin (|{x^3} + x|)$$. Then f is
17
Let a, $$\lambda$$, m $$\in$$ R. Consider the system of linear equations
ax + 2y = $$\lambda$$
3x $$-$$ 2y = $$\mu$$
Which of the following statements is(are) correct?
18
Let $$f:\left[ { - {1 \over 2},2} \right] \to R$$ and $$g:\left[ { - {1 \over 2},2} \right] \to R$$ be function defined by $$f(x) = [{x^2} - 3]$$ and $$g(x) = |x|f(x) + |4x - 7|f(x)$$, where [y] denotes the greatest integer less than or equal to y for $$y \in R$$. Then
Physics
1
A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x0. Consider two cases:
(i) when the block is at x0; and
(ii) when the block is at x = x0 + A.
In both cases, a particle with mass m( < M) is softly placed on the block after which they stick on each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?
(i) when the block is at x0; and
(ii) when the block is at x = x0 + A.
In both cases, a particle with mass m( < M) is softly placed on the block after which they stick on each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?
2
A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at
pressure Pi = 105 Pa and volume Vi = 10-3 m3 changes to a final state at Pf = $$\left( {{1 \over {32}}} \right) \times {10^5}\,Pa$$ and
Vf = 8 $$ \times $$ 10-3 m3 in an adiabatic quasi-static process, such that P3V5 = constant. Consider another
thermodynamic process that brings the system from the same initial state to the same final state in two
steps: an isobaric expansion at Pi followed by an isochoric (isovolumetric) process at volume Vf. The amount of heat supplied to the system in the two-step process is approximately
3
The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires
has a length of 1 m at 10oC. Now the end P is maintained at 10oC, while the end S is heated and
maintained at 400oC. The system is thermally insulated from its surroundings. If the thermal conductivity
of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1.2 $$ \times $$ 10-5 K-1 , the change in length of the wire PQ is
4
Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a
massless, rigid rod of length $$l = \sqrt {24} a$$ through their centers. This assembly is laid on a firm and flat
surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is $$\omega $$. The angular momentum of the entire assembly about the point ‘O’ is $$\overrightarrow L $$ (see the figure). Which of the following statement(s) is(are) true?
5
In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a
periodic motion is $$T = 2\pi \sqrt {{{7\left( {R - r} \right)} \over {5g}}} $$. The values of R and r are measured to be (60 $$ \pm $$ 1) mm and (10 $$ \pm $$ 1)
mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s,
0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of
the following statement(s) is(are) true?
6
There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale.
The Vernier scale of one of the calipers (C1) has 10 equal divisions that correspond to 9 main scale
divisions. The Vernier scale of the other caliper (C2) has 10 equal divisions that correspond to 11 main
scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by
calipers C1 and C2 respectively, are
7
An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?
8
The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by $$E = {3 \over 5}{{Z(Z - 1){e^2}} \over {4\pi {\varepsilon _0}R}}$$
The measured masses of the neutron, $$_1^1H$$, $$_7^{15}N$$ and $$_8^{15}O$$ are 1.008665u, 1.007825u, 15.000109u and 15.003065u, respectively. Given that the radii of both the $$_7^{15}N$$ and $$_8^{15}O$$ nuclei are same, 1 u = 931.5 MeV/c2 (c is the speed of light) and e2/(4$$\pi$$$${{\varepsilon _0}}$$) = 1.44 MeV fm. Assuming that the difference between the binding energies of $$_7^{15}N$$ and $$_8^{15}O$$ is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm = 10$$-$$15 m)
The measured masses of the neutron, $$_1^1H$$, $$_7^{15}N$$ and $$_8^{15}O$$ are 1.008665u, 1.007825u, 15.000109u and 15.003065u, respectively. Given that the radii of both the $$_7^{15}N$$ and $$_8^{15}O$$ nuclei are same, 1 u = 931.5 MeV/c2 (c is the speed of light) and e2/(4$$\pi$$$${{\varepsilon _0}}$$) = 1.44 MeV fm. Assuming that the difference between the binding energies of $$_7^{15}N$$ and $$_8^{15}O$$ is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm = 10$$-$$15 m)
9
A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirror is at an angle $$\theta$$ = 30$$^\circ$$ to the axis of the lens, as shown in the figure.
If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in cm) of the point (x, y) at which the image is formed are
If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in cm) of the point (x, y) at which the image is formed are
10
Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers Rc < R/2, which of the following statement(s) about anyone of the galvanometers is(are) true?
11
A rigid wire loop of square shape having side of length L and resistance R is moving along the X-axis with a constant velocity v0 in the plane of the paper. At t = 0, the right edge of the loop enters a region of length 3L where there is a uniform magnetic field B0 into the plane of the paper, as shown in the figure. For sufficiently large v0, the loop eventually crosses the region. Let x be the location of the right edge of the loop. Let v(x), I(x) and F(x) represent the velocity of the loop, current in the loop, and force on the loop, respectively, as a function of x. Counter-clockwise current is taken as positive.
Which of the following schematic plot(s) is (are) correct? (Ignore gravity)
Which of the following schematic plot(s) is (are) correct? (Ignore gravity)
12
While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the XY-plane containing two small holes that act as two coherent point sources (S1, S2) emitting light of wavelength 600 mm. The student mistakenly placed the screen parallel to the XZ-plane (for z > 0) at a distance D = 3 m from the mid-point of S1S2, as shown schematically in the figure. The distance between the source d = 0.6003 mm. The origin O is at the intersection of the screen and the line joining S1S2.
Which of the following is(are) true of the intensity pattern on the screen?
Which of the following is(are) true of the intensity pattern on the screen?
13
In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is (are) true?
14
Light of wavelength $$\lambda$$ph falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $$\phi$$ and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de-Broglie wavelength of the electrons passing through the anode is $$\lambda$$e, which of the following statement(s) is (are) true?
15
A frame of the reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $$\omega$$ is an example of a non-inertial frame of reference. The relationship between the force $$\overrightarrow F $$rot experienced by a particle of mass m moving on the rotating disc and the force $$\overrightarrow F $$in experienced by the particle in an inertial frame of reference is,
$$\overrightarrow F $$rot = $$\overrightarrow F $$in + 2m ($$\overrightarrow v $$rot $$\times$$ $$\overrightarrow \omega $$) + m ($$\overrightarrow \omega $$ $$\times$$ $$\overrightarrow r $$) $$\times$$ $$\overrightarrow \omega $$,
where, vrot is the velocity of the particle in the rotating frame of reference and r is the position vector of the particle with respect to the centre of the disc.
Now, consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constant angular speed $$\omega$$ about its vertical axis through its centre. We assign a coordinate system with the origin at the centre of the disc, the X-axis along the slot, the Y-axis perpendicular to the slot and the Z-axis along the rotation axis ($$\omega$$ = $$\omega$$ $$\widehat k$$). A small block of mass m is gently placed in the slot at r = (R/2)$$\widehat i$$ at t = 0 and is constrained to move only along the slot.
The distance r of the block at time t is
$$\overrightarrow F $$rot = $$\overrightarrow F $$in + 2m ($$\overrightarrow v $$rot $$\times$$ $$\overrightarrow \omega $$) + m ($$\overrightarrow \omega $$ $$\times$$ $$\overrightarrow r $$) $$\times$$ $$\overrightarrow \omega $$,
where, vrot is the velocity of the particle in the rotating frame of reference and r is the position vector of the particle with respect to the centre of the disc.
Now, consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constant angular speed $$\omega$$ about its vertical axis through its centre. We assign a coordinate system with the origin at the centre of the disc, the X-axis along the slot, the Y-axis perpendicular to the slot and the Z-axis along the rotation axis ($$\omega$$ = $$\omega$$ $$\widehat k$$). A small block of mass m is gently placed in the slot at r = (R/2)$$\widehat i$$ at t = 0 and is constrained to move only along the slot.
The distance r of the block at time t is
16
A frame of the reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $$\omega$$ is an example of a non-inertial frame of reference. The relationship between the force $$\overrightarrow F $$rot experienced by a particle of mass m moving on the rotating disc and the force $$\overrightarrow F $$in experienced by the particle in an inertial frame of reference is,
$$\overrightarrow F $$rot = $$\overrightarrow F $$in + 2m ($$\overrightarrow v $$rot $$\times$$ $$\overrightarrow \omega $$) + m ($$\overrightarrow \omega $$ $$\times$$ $$\overrightarrow r $$) $$\times$$ $$\overrightarrow \omega $$,
where, vrot is the velocity of the particle in the rotating frame of reference and r is the position vector of the particle with respect to the centre of the disc.
Now, consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constant angular speed $$\omega$$ about its vertical axis through its centre. We assign a coordinate system with the origin at the centre of the disc, the X-axis along the slot, the Y-axis perpendicular to the slot and the Z-axis along the rotation axis ($$\omega$$ = $$\omega$$ $$\widehat k$$). A small block of mass m is gently placed in the slot at r = (R/2)$$\widehat i$$ at t = 0 and is constrained to move only along the slot.
The net reaction of the disc on the block is
$$\overrightarrow F $$rot = $$\overrightarrow F $$in + 2m ($$\overrightarrow v $$rot $$\times$$ $$\overrightarrow \omega $$) + m ($$\overrightarrow \omega $$ $$\times$$ $$\overrightarrow r $$) $$\times$$ $$\overrightarrow \omega $$,
where, vrot is the velocity of the particle in the rotating frame of reference and r is the position vector of the particle with respect to the centre of the disc.
Now, consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constant angular speed $$\omega$$ about its vertical axis through its centre. We assign a coordinate system with the origin at the centre of the disc, the X-axis along the slot, the Y-axis perpendicular to the slot and the Z-axis along the rotation axis ($$\omega$$ = $$\omega$$ $$\widehat k$$). A small block of mass m is gently placed in the slot at r = (R/2)$$\widehat i$$ at t = 0 and is constrained to move only along the slot.
The net reaction of the disc on the block is
17
Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r << h. Now, a high voltage source (HV) connected across the conducting plates such that the bottom plate is at +V0 and the top plate at $$-$$V0. Due to their conducting surface, the balls will get charge, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)
Which one of the following statement is correct?
Which one of the following statement is correct?
18
Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r << h. Now, a high voltage source (HV) connected across the conducting plates such that the bottom plate is at +V0 and the top plate at $$-$$V0. Due to their conducting surface, the balls will get charge, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)
The average current in the steady state registered by the ammeter in the circuit will be
The average current in the steady state registered by the ammeter in the circuit will be