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When a simple pendulum is rotated in a vertical plane with constant angular velocity, centripetal force is

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Important Questions on Work, Energy and Power

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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
A particle slides from the top of a smooth hemispherical surface of radius R which is fixed on a horizontal surface. If it separates from the hemisphere at a height h from the horizontal surface, then the speed of the particle is:
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy

A small block slides down from the top of hemisphere of radius R=3 m as shown in the figure. The height h at which the block will lose contact with the surface of the sphere is m. (Assume there is no friction between the block and the hemisphere)

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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is xu2-gL. The value of x is
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to :

(Take the radius of the drum to be 1.25 m and its axle to be horizontal) :
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string is in the ratio 5:1. The velocity of the bob at the highest position is ______ m s-1. (Take g=10 m s-2)
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy

A particle of mass m performs vertical motion in a circle of radius r. Its potential energy at the highest point is ____.

(g is the acceleration due to gravity)

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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break, when
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
A heavy mass is attached at one end of a thin wire and whirled in a vertical circle. The chances of breaking the wire are maximum when
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is α with respect to point P. Which of the following graphs represent the correct relation between A and α when ball goes from Q to R?

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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
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A particle is released on a vertical smooth semicircular track from point X so that, OX makes angle θ  from the vertical (see figure). The normal reaction of the track on the particle vanishes at the point Y where OY makes an angle ϕ with the horizontal. Then
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy

A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB=D. The height h is equal to,
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy

A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m s-1. The length of the pendulum is 0.5 m and mass of the bob is 1 kg. The minimum value of v in m s-1, so that the pendulum describes a circle. (Assume the string to be inextensible and g=10 m s-2 )

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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
Obtain expressions of energy of a particle at different positions in the vertical circular motion.
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
In a Circus, a motor-cyclist having mass of 50 kg moves in a spherical cage of radius 3 m. Calculate the least velocity with which he must pass the highest point without losing contact. Also calculate his angular speed at the highest point.
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
A string of length 1 m is fixed at its one end and a body is attached to the other end of the string. The body oscillates along an arc of a circle in a vertical plane. If the breaking strength of the string is twice the weight of the body, then the maximum distance covered by the body in one oscillation is
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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

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General Science>Physics>Work, Energy and Power>Various Forms of Energy and Law of Conservation of Energy
For a particle moving in vertical circle, the total energy at different positions along the path.