A frictionless wire \(AB\) is fixed on a sphere of radius \(R\). A very small spherical ball slips on this wire. The time taken by this ball to slip from \(A\) to \(B\) is:
          
1. \(\frac{2 \sqrt{g R}}{g \cos \theta}\)
2. \(2 \sqrt{g R} . \frac{\cos \theta}{g}\)
3. \(2 \sqrt{\frac{R}{g}}\)
4. \(\frac{g R}{\sqrt{g\cos \theta}}\)

A body is slipping from an inclined plane of height \(h\) and length \(l\). If the angle of inclination is \(\theta\), the time taken by the body to come from the top to the bottom of this inclined plane is:
1. \(\sqrt{\frac{2 h}{g}}\)
2. \(\sqrt{\frac{2 l}{g}}\)
3. \(\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}\)
4. \(\sin \theta \sqrt{\frac{2 h}{g}}\)

A body sliding on a smooth inclined plane requires \(4\) seconds to reach the bottom starting from the rest at the top. How much time does it take to cover one-fourth distance starting from the rest at the top? 

The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane \(9.8~\text{m}\) long (angle of inclination is $\mathrm{}$\(30^{\circ}\)) is:

A ball is dropped from the top of a tower of 100m height. Simultaneously another ball is thrown upwards from the bottom of the tower with a speed of 50 m/s ($g=10m/s^2$). They will cross each other after:

1. 1 s

2. 2 s

3. 3 s

4. 4 s