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 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. $\theta ={\tan }^{-1}4$

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. $\frac{M+m}{m}l$