Friction and Vertical Circular Motion Problems

Q.

A motorcycle is going on an over-bridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the over-bridge, the normal force on it

1. Increases

2. Decreases

3. Remains the same

4. Fluctuates

Q.

Three identical cars A, B and C are moving at the same speed on three bridges. The car A goes on a plane bridge, B on a bridge convex upward and C goes on a bridge concave upward. Let $F_A,F_{B}and{F}_C$ be the normal forces exerted by the cars on the bridges when they are at the middle of bridges.

1. is maximum of the three forces.

2. = =

3. is maximum of the three forces.

4. is maximum of the three forces.

Q. A piece of wire is bent in the shape of a parabola $y=k{x}^2$ (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stays at rest with respect to the wire, from the y-axis is

1. $\frac{a}{gk}$
2. $\frac{a}{2gk}$
3. $\frac{2a}{gk}$
4. $\frac{a}{4gk}$

Q. A mass $m$ attached to a thin wire is whirled in a vertical circle with a constant speed. The wire is most likely to break when

1. the mass is at the highest point.
2. the wire is horizontal.
3. the mass is at the lowest point.
4. inclined at an angle of $60°$ from vertical.

Q. A bob attached to a light string is rotating in a vertical circle of radius $5\text{m}$. If the velocity of the bob at its lowest point is twice the velocity of the bob when it makes an angle of ${90}^0$ with the vertical. Will the bob complete a full circle? If yes, what is the velocity of the bob at its highest point?

1. The bob will not complete the full circle.
2. The bob will complete the circle and the velocity at the highest point will be $9.12\text{m/s}$.
3. The bob will complete the circle and the velocity at the highest point will be $5.77\text{m/s}$.
4. The bob will complete the circle and the velocity at the highest point will be $7.87\text{m/s}$.

Q. A string attached to a light thread is whirled in a vertical circle with a constant velocity $v$. The radius of the circle is $10\text{m}$. The maximum and minimum tension of the string is in the ratio $4:1$. What is the value of velocity $v$?
(Take $g=10{\text{m/s}}^2$)

1. $15.1\text{m/s}$
2. $12.9\text{m/s}$
3. $13.5\text{m/s}$
4. $10.9\text{m/s}$

Q. A small spherical ball is suspended through a string of length $l$. The whole arrangement is placed in a vehicle which is moving with velocity $v$. Now, suddenly the vehicle stops and ball starts moving along a circular path. If tension in the string at the highest point is twice the weight of the ball then (assume that the ball completes the vertical circle)

1. $v=\sqrt{5gl}$
2. $v=\sqrt{7gl}$
3. velocity of the ball at highest point is $\sqrt{gl}$
4. velocity of the ball at the highest point is $\sqrt{3gl}$

Q. A particle of mass $m$ begins to slide down a fixed smooth sphere from the top as shown. What is its acceleration when it breaks off the sphere?

1. $2g/3$
2. $g/3$
3. $g$
4. $\sqrt{5}g/3$

Q. A body is allowed to slide on a frictionless track from rest position under gravity. The track ends into a circular loop of diameter $D$. What should be the minimum height of the body in terms of $D$ so that it may complete the loop successfully?

1. $\frac{4}{5}D$
2. $\frac{5}{4}D$
3. $1D$
4. $2D$

Q. A string attached to a light thread is whirled in a vertical circle with a constant velocity $v$. The radius of the circle is $10\text{m}$. The maximum and minimum tension of the string is in the ratio $4:1$. What is the value of velocity $v$?
(Take $g=10{\text{m/s}}^2$)

1. $13.5\text{m/s}$
2. $12.9\text{m/s}$
3. $15.1\text{m/s}$
4. $10.9\text{m/s}$