1
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?
A
Both cylinders P and Q reach the ground at the same time.
B
Cylinders P has larger linear acceleration than cylinder Q.
C
Both cylinders reach the ground with same translational kinetic energy.
D
Cylinder Q reaches the ground with larger angular speed.
2
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed $$\omega$$ and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed $${\omega \over 2}$$. The ring and disc are separated by frictionless ball bearings. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of $$30^\circ$$ with the horizontal. Then with respect to the horizontal surface, A
the point O has linear velocity $$3R\omega \widehat i$$
B
the point P has linear velocity $${{11} \over 4}R\omega \widehat i + {{\sqrt 3 } \over 4}R\omega \widehat k$$
C
the point P has linear velocity $${{13} \over 4}R\omega \widehat i - {{\sqrt 3 } \over 4}R\omega \widehat k$$
D
the point P has linear velocity $$\left( {3 - {{\sqrt 3 } \over 4}} \right)R\omega \widehat i + {1 \over 4}R\omega \widehat k$$
3
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Two spherical planets P and Q have the same uniform density r, masses MP and MQ and surface areas A and 4A respectively. A spherical planet R also has uniform density r and its mass is (MP + MQ). The escape velocities from the planets P, Q and R are VP, VQ and VR, respectively. Then
A
VQ > VR > VP
B
VR > VQ > VP
C
$${{{V_R}} \over {{V_P}}} = 3$$
D
$${{{V_P}} \over {{V_Q}}} = {1 \over 2}$$
4
IIT-JEE 2012 Paper 2 Offline
+3
-0.75
A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If $${\rho _c}$$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is
A
more than half-filled if $${\rho _c}$$ is less than 0.5.
B
more than half-filled if $${\rho _c}$$ is more than 1.0.
C
half-filled if $${\rho _c}$$ is more than 0.5.
D
less than half-filled if $${\rho _c}$$ is less than 0.5.
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