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?
A
The center of mass of the assembly rotates about the z-axis with an angular speed of $${\omega \over 5}$$
B
The magnitude of angular momentum of center of mass of the assembly about the point O is $$81\,m{a^2}\omega $$
C
The magnitude of angular momentum of the assembly about its center of mass is $${{17m{a^2}\omega } \over 2}$$
D
The magnitude of the z-component of $$\overrightarrow L $$
is $$55m{a^2}\omega $$
2
JEE Advanced 2016 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
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
A
0.78 mm
B
0.90 mm
C
1.56 mm
D
2.34 mm
3
JEE Advanced 2016 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
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
A
112 J
B
294 J
C
588 J
D
813 J
4
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
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?
A
The amplitude of oscillation in the first case changes by a factor of $$\sqrt {{M \over {m + M}}} $$, whereas in the second case it remains unchanged.
B
The final time period of oscillation in both the cases is same
C
The total energy decreases in both the cases
D
The instantaneous speed at x0 of the combined masses decreases in both the cases
