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Mechanics
Easy
Question
A ring of mass m and radius R is rolling down on a rough inclined plane of angle with horizontal. Plot the angular momentum of the ring about the point of contact of ring and the plane as a function of time.
The correct answer is:
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A spool of mass M and internal and external radii R and 2R hanging from a rope touches a curved surface, as shown. A block of mass m placed on a rough surface inclined at an angle a with horizontal is attached with other end of the rope. The pulley is massless and system is in equilibrium. Find the coefficient of friction
A spool of mass M and internal and external radii R and 2R hanging from a rope touches a curved surface, as shown. A block of mass m placed on a rough surface inclined at an angle a with horizontal is attached with other end of the rope. The pulley is massless and system is in equilibrium. Find the coefficient of friction
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Two point masses A of mass M and B of mass 4M are fixed at the ends of a rod of length l and of negligible mass. The rod is set rotation about an axis perpendicular to its length with a uniform angular speed. The work required for rotating the rod will be minimum when the distance of axis of rotation from the mass A is at
Two point masses A of mass M and B of mass 4M are fixed at the ends of a rod of length l and of negligible mass. The rod is set rotation about an axis perpendicular to its length with a uniform angular speed. The work required for rotating the rod will be minimum when the distance of axis of rotation from the mass A is at
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Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle with AB. Then the moment of inertia of the plate about the axis CD is equal to :
Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle with AB. Then the moment of inertia of the plate about the axis CD is equal to :
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Two light vertical springs with equal natural lengths and spring constants K1 and K2and are separated by a distance l. Their upper ends are fixed to the ceiling and their lower ends to the ends A and B of a light horizontal rod AB. A vertical downwards force F is applied at point C on the rod. AB will remain horizontal in equilibrium if the distance AC is :
Two light vertical springs with equal natural lengths and spring constants K1 and K2and are separated by a distance l. Their upper ends are fixed to the ceiling and their lower ends to the ends A and B of a light horizontal rod AB. A vertical downwards force F is applied at point C on the rod. AB will remain horizontal in equilibrium if the distance AC is :
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A homogeneous rod AB of length L and mass M is hinged at the centre O in such a way that it can rotate freely in the vertical plane. The rod is initially in horizontal position. An insect S of the same mass M falls vertically with speed V on point C, midway between the points O and B. Immediately after falling, the insect starts to move towards B such that the rod rotates with a constant angular velocity 
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If insect reaches the end B when the rod has turned through an angle of calculate V in terms of L
A homogeneous rod AB of length L and mass M is hinged at the centre O in such a way that it can rotate freely in the vertical plane. The rod is initially in horizontal position. An insect S of the same mass M falls vertically with speed V on point C, midway between the points O and B. Immediately after falling, the insect starts to move towards B such that the rod rotates with a constant angular velocity .
If insect reaches the end B when the rod has turned through an angle of calculate V in terms of L
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A homogeneous rod AB of length L and mass M is hinged at the centre O in such a way that it can rotate freely in the vertical plane. The rod is initially in horizontal position. An insect S of the same mass M falls vertically with speed V on point C, midway between the points O and B. Immediately after falling, the insect starts to move towards B such that the rod rotates with a constant angular velocity .
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A homogeneous rod AB of length L and mass M is hinged at the centre O in such a way that it can rotate freely in the vertical plane. The rod is initially in horizontal position. An insect S of the same mass M falls vertically with speed V on point C, midway between the points O and B. Immediately after falling, the insect starts to move towards B such that the rod rotates with a constant angular velocity .
Calculate angular velocity in terms of V and L
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A man of mass 100 kg stands at the rim of a turn table of radius 2m, moment of inertia 4000 kg. The table is mounted on a vertical smooth axis, through its center. The whole system is initially at rest. The man now walks on table with a velocity 1 m/s relative to earth
Through what angle will it have rotated when the man reaches his initial position relative to earth
A man of mass 100 kg stands at the rim of a turn table of radius 2m, moment of inertia 4000 kg. The table is mounted on a vertical smooth axis, through its center. The whole system is initially at rest. The man now walks on table with a velocity 1 m/s relative to earth
Through what angle will it have rotated when the man reaches his initial position relative to earth
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A man of mass 100 kg stands at the rim of a turn table of radius 2m, moment of inertia 4000 kg. The table is mounted on a vertical smooth axis, through its center. The whole system is initially at rest. The man now walks on table with a velocity 1 m/s relative to earth
Through what angle will the turn table have rotated when the man reaches his initial position on it
A man of mass 100 kg stands at the rim of a turn table of radius 2m, moment of inertia 4000 kg. The table is mounted on a vertical smooth axis, through its center. The whole system is initially at rest. The man now walks on table with a velocity 1 m/s relative to earth
Through what angle will the turn table have rotated when the man reaches his initial position on it
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A man of mass 100 kg stands at the rim of a turn table of radius 2m, moment of inertia 4000 kg. The table is mounted on a vertical smooth axis, through its center. The whole system is initially at rest. The man now walks on table with a velocity 1 m/s relative to earth
With what angular velocity will the turn table rotate
A man of mass 100 kg stands at the rim of a turn table of radius 2m, moment of inertia 4000 kg. The table is mounted on a vertical smooth axis, through its center. The whole system is initially at rest. The man now walks on table with a velocity 1 m/s relative to earth
With what angular velocity will the turn table rotate
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A string is wrapped several times on a cylinder of mass M and radius R. the cylinder is pivoted about its axis of symmetry. A block of mass m tied to the string rests on a support so that the string is slack. the block is lifted up to a height h and the support is removed. (shown in figure)
If M = m, what fraction of KE is lost due to the jerk developed in the string
A string is wrapped several times on a cylinder of mass M and radius R. the cylinder is pivoted about its axis of symmetry. A block of mass m tied to the string rests on a support so that the string is slack. the block is lifted up to a height h and the support is removed. (shown in figure)
If M = m, what fraction of KE is lost due to the jerk developed in the string
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A string is wrapped several times on a cylinder of mass M and radius R. the cylinder is pivoted about its axis of symmetry. A block of mass m tied to the string rests on a support so that the string is slack. the block is lifted up to a height h and the support is removed. (shown in figure)
When the string experience a jerk, a large impulsive force is generated for a short duration, so that contribution of weight mg can be neglected during this duration. Then what will be speed of block m, just after string has become taut
A string is wrapped several times on a cylinder of mass M and radius R. the cylinder is pivoted about its axis of symmetry. A block of mass m tied to the string rests on a support so that the string is slack. the block is lifted up to a height h and the support is removed. (shown in figure)
When the string experience a jerk, a large impulsive force is generated for a short duration, so that contribution of weight mg can be neglected during this duration. Then what will be speed of block m, just after string has become taut
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A string is wrapped several times on a cylinder of mass M and radius R. the cylinder is pivoted about its axis of symmetry. A block of mass m tied to the string rests on a support so that the string is slack. the block is lifted up to a height h and the support is removed. (shown in figure)
What is the angular velocity of cylinder just before the string becomes taut
A string is wrapped several times on a cylinder of mass M and radius R. the cylinder is pivoted about its axis of symmetry. A block of mass m tied to the string rests on a support so that the string is slack. the block is lifted up to a height h and the support is removed. (shown in figure)
What is the angular velocity of cylinder just before the string becomes taut
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A wheel is under pure rotational motion about an axis passing through its centre. It moves with constant angular velocity.
A wheel is under pure rotational motion about an axis passing through its centre. It moves with constant angular velocity.
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A rod of length ‘l’ is pivoted smoothly at O is resting on a block of height h. If the block moves with a constant velocity V, pick the current alternatives.
A rod of length ‘l’ is pivoted smoothly at O is resting on a block of height h. If the block moves with a constant velocity V, pick the current alternatives.
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