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Easy
Question
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 :
The correct answer is:
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A planar object made up of a uniform square plate and four semicircular discs of the same thickness and material is being acted upon by four forces of equal magnitude as shown in figure. The coordinates of point of application of forces is given by
A planar object made up of a uniform square plate and four semicircular discs of the same thickness and material is being acted upon by four forces of equal magnitude as shown in figure. The coordinates of point of application of forces is given by
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In the figure shown a ball rolls without sliding. On a horizontal surface. It ascends a curved track up to height h and returns. Value of h is 
for sufficiently rough curved track to avoid sliding and for smooth curved track, then:
In the figure shown a ball rolls without sliding. On a horizontal surface. It ascends a curved track up to height h and returns. Value of h is for sufficiently rough curved track to avoid sliding and for smooth curved track, then:
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A smooth tube of certain mass is rotated in gravity free space and released. The two balls shown in the figure move towards ends of the tube. For the whole system which of the following quantity is not conserved?
A smooth tube of certain mass is rotated in gravity free space and released. The two balls shown in the figure move towards ends of the tube. For the whole system which of the following quantity is not conserved?
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In the pulley system shown, if radii of the bigger and smaller pulley are 2 m and 1m respectively and the acceleration of block A is 5 
in the downward direction, then the acceleration of block B will be:
In the pulley system shown, if radii of the bigger and smaller pulley are 2 m and 1m respectively and the acceleration of block A is 5 in the downward direction, then the acceleration of block B will be:
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A uniform thin rod of length 
, mass 4m is bent at the points as shown in the figure. What is the moment of inertia of the rod about the axis passing through point O & perpendicular to the plane of the paper?
A uniform thin rod of length , mass 4m is bent at the points as shown in the figure. What is the moment of inertia of the rod about the axis passing through point O & perpendicular to the plane of the paper?
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A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is mass less and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity 
. The coefficient of friction is 
.The maximum value of v0 for which the disk will roll without slipping is
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is mass less and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity . The coefficient of friction is .The maximum value of v0 for which the disk will roll without slipping is
physics-General
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A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is mass less and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity . The coefficient of friction is . The centre of mass of the disk undergoes simple harmonic motion with angular frequency 
equal to
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is mass less and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity . The coefficient of friction is . The centre of mass of the disk undergoes simple harmonic motion with angular frequency equal to
physics-General
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A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is mass less and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity . The coefficient of friction is The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is mass less and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity . The coefficient of friction is The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is
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A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then
A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then
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A ball moves over a fixed track as shown in the figure. From A to B the ball rolls without slipping. If surface BC is frictionless and 
and 
are kinetic energy of the ball at A, B and C respectively, then:-
A ball moves over a fixed track as shown in the figure. From A to B the ball rolls without slipping. If surface BC is frictionless and and are kinetic energy of the ball at A, B and C respectively, then:-
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A solid sphere is in pure rolling motion on an inclined surface having inclination 
:
A solid sphere is in pure rolling motion on an inclined surface having inclination :
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A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of 
with respect to the initial position. The object is :-
A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of with respect to the initial position. The object is :-
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A solid sphere of radius R has moment of inertia I about its geometrical axis. If it is melted into a disc of radius r and thickness t. If it's moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to I, then the value of r is equal to :-
A solid sphere of radius R has moment of inertia I about its geometrical axis. If it is melted into a disc of radius r and thickness t. If it's moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to I, then the value of r is equal to :-
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From a circular disc of radius R and mass 9M, a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is :
From a circular disc of radius R and mass 9M, a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is :
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A disc is rolling (with slipping) on a horizontal surface. C is its centre and Q and P are two points equidistant from C. Let 
, 
and 
be the magnitude of velocities of points P, Q and C respectively, then :
A disc is rolling (with slipping) on a horizontal surface. C is its centre and Q and P are two points equidistant from C. Let , and be the magnitude of velocities of points P, Q and C respectively, then :
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