A ball rolls off top of a staircase with a horizontal velocity u m/s. If the steps are h metre high and b mere wide, the ball will just hit the edge of nth step if n equals to
1. \(\dfrac{h u^2}{g b^2}\)
2. \(\dfrac{u^2 8}{g b^2}\)
3. \(\dfrac{2 h u^2}{g b^2}\)
4. \(\dfrac{2 u^2 g}{h b^2}\)

A man standing on the roof of a house of height h throws one particle vertically downwards and another particle horizontally with the same velocity \(u.\) The ratio of their velocities when they reach the earth’s surface will be
1. \(\sqrt{2 g h+u^2}: u\)
2. \(1: 2\)
3. \(1:1\)
4. \(\sqrt{2 g h+u^2}: \sqrt{2 g}\)

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

A particle has an initial velocity (\(2\hat{i}+3\hat{j}\)) and an acceleration (\(0.3\hat{i}+0.2\hat{j}\)). The magnitude of velocity after \(10\) s will be:
1. \(9 \sqrt{2} ~\text{units} \)
2. \(5 \sqrt{2} ~\text{units} \)
3. \(5 ~\text{units} \)
4. \(9~\text{units} \)

A particle has an initial velocity $\left(3\hat{i}+4\hat{j}\right)$ and has an acceleration $\left(0.4\hat{i}+0.3\hat{j}\right)$. Its speed after 10 s is: 
1. \(7\) unit
2. \(7\sqrt{2}\) unit
3. \(8\) unit
4. \(8\sqrt{2}\) unit

Drops of water fall from the roof of a building 20 m high at regular intervals

of time. The first drop reaching the ground at the same instant fifth drop

starts its fall. What are the distance  of second and third drops from roof? (g =

10 $m/s^2$)

1. 5.0 m and 1.25 m

2. 5.0 m and 2.25 m

3. 11.25 m and 5.0 m

4. 11.25 and 1.25 m