HARD
JEE Advanced
IMPORTANT
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A small roller of diameter 20 cm has an axle of diameter 10 cm (see figure below on the left). It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of the axle (see figure on the right). The scale is now pushed slowly on the axle so that it moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has moved 50 cm, the position of the scale will look like (figures are schematic and not drawn to scale)

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Important Questions on Rotational Motion

HARD
JEE Advanced
IMPORTANT
Consider a body of mass 1.0kg at rest at the origin at time t=0. A force F=αti^+βj^ is applied on the body, where α=1.0Ns-1 and β=1.0 N. The torque acting on the body about the origin at time =1.0 s is τ. Which of the following statements is (are) true?
HARD
JEE Advanced
IMPORTANT
A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle 60° with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is 2-310 s, then the height of the top of the inclined plane (in meters) is __________. Take g=10 m s-2.
MEDIUM
JEE Advanced
IMPORTANT
A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at x=0, in a coordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block its position is x and velocity is v. At that instant, which of the following options is correct?
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HARD
JEE Advanced
IMPORTANT
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 30o 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 hl and the frictional force f at the bottom of the stick are: g=10 m s-2
HARD
JEE Advanced
IMPORTANT
The position vector r of a particle of mass m is given by the following equation rt=αt3i^+βt2j^, where α=103 m s-3, β=5 m s-2 and m=0.1 kg. At t=1s, which of the following statements (s) is (are) true about the particle?
MEDIUM
JEE Advanced
IMPORTANT
A ring of mass M and radius R is rotating with angular speed ω about a fixed vertical axis passing through its centre O with two point masses each of mass M8 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 89ω and one of the masses is at a distance of 35R from O. At this instant the distance of the other mass from O is


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