A metal ring of mass m and radius R is placed on smooth horizontal table and is set rotating about its own axis in such a way that each part of the ring moves with a speed v. Tension in the ring is:

1. $\frac{m{v}^2}{R}$

2. $\frac{m{v}^2}{2R}$

3. $\frac{m{v}^2}{2\mathrm{\pi }R}$

4. None of these

A body moves along an uneven surface with constant speed at all points. The normal reaction due to ground on the body is:

A cyclist turns around a curve at 15 miles/hour. If he turns at double the speed, the tendency to overturn is  

1. Doubled

2. Quadrupled

3. Halved

4. Unchanged

If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be

1. $mg+\frac{m{v}^2}{r}$

2. $mg-\frac{m{v}^2}{r}$

3. $\frac{m^2{v}^{2}g}{r}$

4. $\frac{v^{2}g}{r}$

A car sometimes overturns while taking a turn. When it overturns, it is:

1. the inner wheel which leaves the ground first.

2. the outer wheel which leaves the ground first.

3. both the wheels leave the ground simultaneously.

4. either wheel leaves the ground first.

A motor cyclist moving with a velocity of 72 km/hour on a flat road takes a turn on the road at a point where the radius of curvature of the road is 20 meters. The acceleration due to gravity is 10 m/sec². In order to avoid skidding, he must not bend with respect to the vertical plane by an angle greater than 

1. $\theta ={\tan }^{-1}6$

2. $\theta ={\tan }^{-1}2$

3. $\theta ={\tan }^{-1}25.92$

4. $\theta ={\tan }^{-1}4$

A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance ‘r’. The speed of the particle is 

1. Proportional to r²

2. Independent of r

3. Proportional to r

4. Proportional to 1/r

Two masses M and m are attached to a vertical axis by weightless threads of combined length l. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity ω. If the tensions in the threads are the same during motion, the distance 'x' of M from the axis is- 

1. $\frac{Ml}{M+m}$

2. $\frac{ml}{M+m}$

3. $\frac{M+m}{M}l$

4. $\frac{M+m}{m}l$

A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/hr. The centripetal force is 

1. 250 N

2. 750 N

3. 1000 N

4. 1200 N

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved 

1. 14 m/s

2. 3 m/s

3. 3.92 m/s

4. 5 m/s