# Circular Motion

## 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 to 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

Q: 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 to 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

Ans: (d)

## A bob of mass M is suspended by a massless string of length L. The horizontal velocity v at position A is just sufficient to make it reach at the point B. The angle θ at which the speed of the bob is half of that at point A, satisfies

Q: A bob of mass M is suspended by a massless string of length L. The horizontal velocity v at position A is just sufficient to make it reach at the point B. The angle θ at which the speed of the bob is half of that at point A, satisfies

(a) θ = π/4

(b) π/4 < θ < π/2

(c) π/2 < θ < 3π/4

(d) 3π/4 < θ < π

Ans: (c)

## A particle of mass m initially at the point A at the centre level of a fixed smooth hollow sphere of radius R is given an upward velocity v0 along the internal surface of the sphere. The particle is just able to complete the vertical circle. Then,

Q: A particle of mass m initially at the point A at the centre level of a fixed smooth hollow sphere of radius R is given an upward velocity v0 along the internal surface of the sphere. The particle is just able to complete the vertical circle. Then,

(a) The value of v0 is $\sqrt{5 g R}$

(b) The value of v0 is $\sqrt{3 g R}$

(c) The velocity of the particle at the highest point is zero

(d) The normal reaction at the highest point is zero.

Ans: (b) , (d)

## A ball of mass m = 1 kg is tied to a string of length l = 1 m and a horizontal force is applied on it, which initially, is zero and gradually increases until string becomes inclined at an angle θ = 60° with vertical as shown in figure. Find the work done by the force.

Q: A ball of mass m = 1 kg is tied to a string of length l = 1 m and a horizontal force is applied on it, which initially, is zero and gradually increases until string becomes inclined at an angle θ = 60° with vertical as shown in figure. Find the work done by the force.

(a) zero

(b) Non- zero

(c) 5 J

(d) 10 J

Ans: (c)

## A particle of mass m is moving on a circular path of radius r in the influence of force F = (-k)/r^2 r ̂, where k is a positive constant.

Q: A particle of mass m is moving on a circular path of radius r in the influence of force $F = \frac{-k}{r^2} \hat{r}$ , where k is a positive constant.

(a) Kinetic energy of particle is k/r

(b) Kinetic energy of particle k/2r

(c) Potential energy of particle is (-k)/(r )

(d) Total mechanical energy of particle is (– k )/2r