1
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
A ring of mass M and radius R is rotating with angular speed $$\omega$$ about a fixed vertical axis passing through its centre O with two point masses each of mass $${M \over 8}$$ at rest at O. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant, the angular speed of the system is $${8 \over 9}$$$$\omega$$ and one of the masses is at a distance of $${3 \over 5}$$R from O. At this instant, the distance of the other mass from O is
A
$${2 \over 3}$$R
B
$${1 \over 3}$$R
C
$${3 \over 5}$$R
D
$${4 \over 5}$$R
2
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.
3
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 $$\left( {3 - {{\sqrt 3 } \over 4}} \right)R\omega \widehat i + {1 \over 4}R\omega \widehat k$$
4
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.
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