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A disc of mass m and radius R moves in the x-y plane as shown in. The angular momentum of the disc about the origin O at the instant shown is
The correct answer is:
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Moment of inertia of a rectangular plate about an axis passing through P and perpendicular to the plate is I. Then moment of PQR about an axis perpendicular to the plane of the plate:
Moment of inertia of a rectangular plate about an axis passing through P and perpendicular to the plate is I. Then moment of PQR about an axis perpendicular to the plane of the plate:
physics-General
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A square plate of edge a/2 is cut out from a uniform square plate of edge ' a ' as shown in figure. The mass of the remaining portion is M. The moment of inertia of the shaded portion about an axis passing through ' O ' (centre of the square of side (A) and perpendicular to plane of the plate is
A square plate of edge a/2 is cut out from a uniform square plate of edge ' a ' as shown in figure. The mass of the remaining portion is M. The moment of inertia of the shaded portion about an axis passing through ' O ' (centre of the square of side (A) and perpendicular to plane of the plate is
physics-General
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The fig shows a uniform rod lying along the x-axis. The locus of all the points lying on the xy-plane, about which the moment of inertia of the rod is same as that about O is :
The fig shows a uniform rod lying along the x-axis. The locus of all the points lying on the xy-plane, about which the moment of inertia of the rod is same as that about O is :
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A thin rod of length 4l, mass 4 m is bent at the points as shown in the fig. What is the moment of inertia of the rod about the axis passing point O& perpendicular to the plane of the paper.
A thin rod of length 4l, mass 4 m is bent at the points as shown in the fig. What is the moment of inertia of the rod about the axis passing point O& perpendicular to the plane of the paper.
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Figure below shows the variation of the moment of inertia of a uniform rod about an axis normal to its length with the distance of the axis from the end of the rod. The moment of inertia of the rod about an axis passing through its centre and perpendicular to the its length is :
Figure below shows the variation of the moment of inertia of a uniform rod about an axis normal to its length with the distance of the axis from the end of the rod. The moment of inertia of the rod about an axis passing through its centre and perpendicular to the its length is :
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Two thin rods of mass 
and length l each are joined to form l shape as shown. The moment of inertia of rods about an axis passing through free end (O) of a rod and perpendicular to both the rods is:
Two thin rods of mass and length l each are joined to form l shape as shown. The moment of inertia of rods about an axis passing through free end (O) of a rod and perpendicular to both the rods is:
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A right triangular plate 
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A right triangular plate of mass is free to rotate in the vertical plane about a fixed horizontal axis through A. It is supported by a string such that the side AB is horizontal. The reaction at the support A is
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A cylinder of mass m suspended by two strings wrapped around the cylinder one near each end, the free ends of the strings being attached to hooks on the ceiling, such that the length of the cylinder is horizontal, From the position of rest, the cylinder is allowed to roll down as suspension strings unwind. Then calculate the time dependence of the instantaneous power developed by gravity
A cylinder of mass m suspended by two strings wrapped around the cylinder one near each end, the free ends of the strings being attached to hooks on the ceiling, such that the length of the cylinder is horizontal, From the position of rest, the cylinder is allowed to roll down as suspension strings unwind. Then calculate the time dependence of the instantaneous power developed by gravity
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A man pushes a cylinder of mass 
with the help of a plank of mass 
as shown. There is no slipping at any contact. The horizontal component of the force applied by the man is F. The acceleration of the plank
A man pushes a cylinder of mass with the help of a plank of mass as shown. There is no slipping at any contact. The horizontal component of the force applied by the man is F. The acceleration of the plank
physics-General
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In the fig shown mass of both, the spherical body and block is m. Moment of inertia of the spherical body about centre of mass is 
. The spherical body rolls on the horizontal surface. There is no slipping at any surfaces in contact. The ratio of kinetic energy of the spherical body to that of block is
In the fig shown mass of both, the spherical body and block is m. Moment of inertia of the spherical body about centre of mass is . The spherical body rolls on the horizontal surface. There is no slipping at any surfaces in contact. The ratio of kinetic energy of the spherical body to that of block is
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A solid sphere rolls without slipping along the track shown in fig. The sphere starts from rest from a height h above the bottom of a loop radius R which is much larger than the radius of the sphere r. The minimum value of h for the sphere to complete the loop is
A solid sphere rolls without slipping along the track shown in fig. The sphere starts from rest from a height h above the bottom of a loop radius R which is much larger than the radius of the sphere r. The minimum value of h for the sphere to complete the loop is
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The acceleration a of the plank p required to keep the centre C of a cylinder in a fixed position during the motion is no slipping takes place between cylinder and plank)
The acceleration a of the plank p required to keep the centre C of a cylinder in a fixed position during the motion is no slipping takes place between cylinder and plank)
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A billiard ball of radius R is struck by a cue as shown. Assume that the impulse given by the cue is purely horizontal. For the ball to roll without any initial slippage
A billiard ball of radius R is struck by a cue as shown. Assume that the impulse given by the cue is purely horizontal. For the ball to roll without any initial slippage
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A cylinder of mass m and radius R is rolling without slipping on a horizontal surface with angular velocity 
. The velocity of centre of mass of cylinder is 
. The cylinder comes across a step of height .(Assume required friction is present at edge of the step.) angular velocity of cylinder just after the collision is (Assume cylinder remains in contact and no slipping occurs at the edge of the step)
A cylinder of mass m and radius R is rolling without slipping on a horizontal surface with angular velocity . The velocity of centre of mass of cylinder is . The cylinder comes across a step of height .(Assume required friction is present at edge of the step.) angular velocity of cylinder just after the collision is (Assume cylinder remains in contact and no slipping occurs at the edge of the step)
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A Cylinder of radius R is spinned and then placed on an incline having coefficient of friction 
is the angle of incline). The cylinder continues to spin without falling for time
A Cylinder of radius R is spinned and then placed on an incline having coefficient of friction is the angle of incline). The cylinder continues to spin without falling for time
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