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A uniform rod of length 1 is pivoted at point A. It is struck by a horizontal force which delivers an impulse J at a distance x from point A as shown in fig, impulse delivered by pivot is zero if x is equal to
The correct answer is:
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A rod AB of length 1 m is placed at the edge of a smooth table as shown in fig. It is hit horizontally at point B. If the displacement of centre of mass in 1 s is 
. The angular velocity of the rod is 
A rod AB of length 1 m is placed at the edge of a smooth table as shown in fig. It is hit horizontally at point B. If the displacement of centre of mass in 1 s is . The angular velocity of the rod is
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A small block of mass ' m ' is rigidly attached at ' P ' to a ring of mass ' 3 m ' and radius ' r '. The system is released from rest at 
and rolls without sliding. The angular acceleration of hoop just after releases is -
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A smooth horizontal tube of length l rotates about a vertical axis as shown. A particle placed at the extreme end of the tube is projected towards 0 with a velocity 
, while at the same time the tube rotates about the axis with constant angular speed 
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A smooth horizontal tube of length l rotates about a vertical axis as shown. A particle placed at the extreme end of the tube is projected towards 0 with a velocity , while at the same time the tube rotates about the axis with constant angular speed . The path of the particle is given by
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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
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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:
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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
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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 :
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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 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 
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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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