1
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-1
A length-scale (l) depends on the permittivity ($$\varepsilon $$) of a dielectric material, Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for I is(are) dimensionally correct?
A
$$l = \sqrt {\left( {{{n{q^2}} \over {\varepsilon {k_b}T}}} \right)} $$
B
$$l = \sqrt {\left( {{{\varepsilon {k_b}T} \over {n{q^2}}}} \right)} $$
C
$$l = \sqrt {\left( {{{{q^2}} \over {\varepsilon {n^{2/3}}{k_B}T}}} \right)} $$
D
$$l = \sqrt {\left( {{{{q^2}} \over {\varepsilon {n^{1/3}}{k_B}T}}} \right)} $$
2
JEE Advanced 2016 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
A uniform wooden stick of mass 1.6 kg and length $$l$$ rests in an inclined manner on a smooth, vertical wall of height h ( < $$l$$ ) such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $$30^\circ $$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio $${h \over l}$$ and the frictional force f at the bottom of the stick are ( g =10 ms-2 )
A
$${h \over l} = {{\sqrt 3 } \over {16}},f = {{16\sqrt 3 } \over 3}N$$
B
$${h \over l} = {3 \over {16}},f = {{16\sqrt 3 } \over 3}N$$
C
$${h \over l} = {{3\sqrt 3 } \over {16}},f = {{8\sqrt 3 } \over 3}N$$
D
$${h \over l} = {{3\sqrt 3 } \over {16}},f = {{16\sqrt 3 } \over 3}N$$
3
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
The position vector $$\overrightarrow r $$ of a particle of mass m is given by the following equation $$$\overrightarrow r \left( t \right) = \alpha {t^3}\widehat i + \beta {t^2}\widehat j,$$$where $$\alpha = {{10} \over 3}m{s^{ - 3}}$$, $$\beta = 5\,m{s^{ - 2}}$$ and m = 0.1 kg. At t = 1 s, which of the following statement(s) is(are) true about the particle?
A
The velocity $$\overrightarrow v $$ is given by $$\overrightarrow v = \left( {10\widehat i + 10\widehat j} \right)$$ ms-1
B
The angular momentum $$\overrightarrow L $$ with respect to the origin is given by $$\overrightarrow L = - \left( {{5 \over 3}} \right)\widehat k\,N\,m\,s$$
C
The force $$\overrightarrow F $$ is given by $$\overrightarrow F = \left( {\widehat i + 2\widehat j} \right)N$$
D
The torque $$\overrightarrow \tau $$ with respect to the origin is given by $$\overrightarrow \tau = - \left( {{{20} \over 3}} \right)\widehat k\,N\,m$$
4
JEE Advanced 2016 Paper 1 Offline
Numerical
+3
-0
Consider two solid spheres P and Q each of density 8 gm cm–3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm–3 and viscosity $$\eta $$ = 3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm–3 and viscosity $$\eta $$ = 2 poiseulles. The ratio of the terminal velocities of P and Q is
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