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Easy
Question
A disc of radius R rolls without slipping at speed 
along positive x-axis. Velocity of point P at the instant shown in fig is
The correct answer is:
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Fig shows smooth inclined plane of inclination 
fixed in a car. A sphere is set in pure rolling on the incline. For what value of a the acceleration of car in horizontal direction) the sphere will continue pure rolling.
Fig shows smooth inclined plane of inclination fixed in a car. A sphere is set in pure rolling on the incline. For what value of a the acceleration of car in horizontal direction) the sphere will continue pure rolling.
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The arrangement shown in figure consists of two identical uniform solid cylinders, each of mass m, on which two light threads are wound symmetrically. Find the tension of each thread in the process of motion. The friction in the axile of the upper cylinder is assumed to be absent.
The arrangement shown in figure consists of two identical uniform solid cylinders, each of mass m, on which two light threads are wound symmetrically. Find the tension of each thread in the process of motion. The friction in the axile of the upper cylinder is assumed to be absent.
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A uniform cylinder of mass M and radius R rolls without slipping down a slope of angle 
with horizontal. The cylinder is connected to a spring of force constant k at the centre, the other side of which is connected to a fixed support at A. The cylinder is released when the spring is unstretched. The force of friction f)
A uniform cylinder of mass M and radius R rolls without slipping down a slope of angle with horizontal. The cylinder is connected to a spring of force constant k at the centre, the other side of which is connected to a fixed support at A. The cylinder is released when the spring is unstretched. The force of friction f)
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A plank P is placed on a hollow cylinder C, which rolls on a horizontal surface as shown. No slippage is there at any of the surface in contact. Both have equal mass say M each) and if v is the velocity of centre of mass of the cylinder C, then the ratio of the kinetic energy of plank P to the cylinder C is
A plank P is placed on a hollow cylinder C, which rolls on a horizontal surface as shown. No slippage is there at any of the surface in contact. Both have equal mass say M each) and if v is the velocity of centre of mass of the cylinder C, then the ratio of the kinetic energy of plank P to the cylinder C is
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A uniform thin ring ABCD rolls without slipping on a rough horizontal surface, The line BD is horizontal and line AC is vertical. The kinetic energies of section AB, BC, CD and DA are respectively 
and 
. It follows that :
A uniform thin ring ABCD rolls without slipping on a rough horizontal surface, The line BD is horizontal and line AC is vertical. The kinetic energies of section AB, BC, CD and DA are respectively and . It follows that :
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A cylinder execute pure rolling without slipping with a constant velocity on a plank, whose upper surface is rough enough, but lower surface is smooth. The plank is kept at rest on a smooth horizontal surface by the application of an external force F. Choose the correct alternative :
A cylinder execute pure rolling without slipping with a constant velocity on a plank, whose upper surface is rough enough, but lower surface is smooth. The plank is kept at rest on a smooth horizontal surface by the application of an external force F. Choose the correct alternative :
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A billiard player hits a billiard ball of mass m and radius r lying at rest on the billiard table. When the cue hits the ball horizontally with force F at height (r+h) from the table top the ball rolls without slipping h is given as
A billiard player hits a billiard ball of mass m and radius r lying at rest on the billiard table. When the cue hits the ball horizontally with force F at height (r+h) from the table top the ball rolls without slipping h is given as
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Angular acceleration of the cylinder C shown if Fig. (all strings and pulley are ideal) :
Angular acceleration of the cylinder C shown if Fig. (all strings and pulley are ideal) :
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A slender rod of mass m and length L is pivoted about a horizontal axis through one end and released from rest at an angle of 30° above the horizontal. The force exerted by the pivot on the rod at the instant when the rod passes through a horizontal position is
A slender rod of mass m and length L is pivoted about a horizontal axis through one end and released from rest at an angle of 30° above the horizontal. The force exerted by the pivot on the rod at the instant when the rod passes through a horizontal position is
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A uniform rod AB rests on a smooth floor leaning against a smooth wall. The rod AB is released when is small. the instantaneous centre of rotation always lies in the :
A uniform rod AB rests on a smooth floor leaning against a smooth wall. The rod AB is released when is small. the instantaneous centre of rotation always lies in the :
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Each pulley in below has radius r and moment of inertia I. The acceleration of the block is (M>m)
Each pulley in below has radius r and moment of inertia I. The acceleration of the block is (M>m)
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A Constant force acting at the centre of a uniform disc of radius r is always perpendicular to the plane of the disc. The disc can rotate about a chord at a distance x from the centre of the disc. For what value of x will the angular acceleration of the disc be maximum?
A Constant force acting at the centre of a uniform disc of radius r is always perpendicular to the plane of the disc. The disc can rotate about a chord at a distance x from the centre of the disc. For what value of x will the angular acceleration of the disc be maximum?
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Two identical particles B and C each of mass 50 g are connected by a light rod of length 30 cm. Another particle A has same mass moving with a speed u=60 cm/s strikes B, in a direction perpendicular to AB. and sticks to it. The whole, process takes place on a smooth horizontal plane. The angular momentum L and angular velocity 
of the system its centre of mass, immediately after the impact is given by ( in SI units)
Two identical particles B and C each of mass 50 g are connected by a light rod of length 30 cm. Another particle A has same mass moving with a speed u=60 cm/s strikes B, in a direction perpendicular to AB. and sticks to it. The whole, process takes place on a smooth horizontal plane. The angular momentum L and angular velocity of the system its centre of mass, immediately after the impact is given by ( in SI units)
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A uniform disc rotates freely about a perpendicular axis making 
revolutions per minute. wax of mass m falls vertically and sticks to the disc at distance x from the axis Rotational speed reduced to 
, then moment of inertia of the disc is
A uniform disc rotates freely about a perpendicular axis making revolutions per minute. wax of mass m falls vertically and sticks to the disc at distance x from the axis Rotational speed reduced to , then moment of inertia of the disc is
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Two similar beads each of mass m slide smoothly along a uniform rod mass M and length l. the rod can rotate along an axis passing through its centre and normal to its length. Initially the rod is rotated with angular speed 
when beads are at the centre C of the rod. The angular speed 
of the rod when beads slide to the two ends of the rod without any external force is given by
Two similar beads each of mass m slide smoothly along a uniform rod mass M and length l. the rod can rotate along an axis passing through its centre and normal to its length. Initially the rod is rotated with angular speed when beads are at the centre C of the rod. The angular speed of the rod when beads slide to the two ends of the rod without any external force is given by
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