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 2011 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

A metal rod of length L and mass m is pivoted at one end. A thin disk of mass M and radius R ( < L) is attached at its centre to the free end of the rod. Consider two ways the disc is attached : (case A). The disc is not free to rotate about its centre and (case B) the disc is free to rotate about its centre. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is(are) true?

A
Restoring torque in case A = Restoring torque in case B.
B
Restoring torque in case A < Restoring torque in case B.
C
Angular frequency for case A > Angular frequency for case B.
D
Angular frequency for case A < Angular frequency for case B.
4
IIT-JEE 2009 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure below, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then,

A
$${\overrightarrow V _C} - {\overrightarrow V _A} = 2({\overrightarrow V _B} - {\overrightarrow V _C})$$
B
$${\overrightarrow V _C} - {\overrightarrow V _B} = {\overrightarrow V _B} - {\overrightarrow V _A}$$
C
$$|{\overrightarrow V _C} - {\overrightarrow V _A}| = 2|{\overrightarrow V _B} - {\overrightarrow V _C}|$$
D
$$|{\overrightarrow V _C} - {\overrightarrow V _A}| = 4|{\overrightarrow V _B}|$$
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