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 man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4 sec his displacement relative to the ground will be

1. 5  m

2. 4.8 m

3. 3.2 m

4. 3.0 m

A particle is projected at an angle $\theta$ with horizontal with an initital speed u. When it makes an angle $\alpha$ with horizontal, its speed v is-

1. $u\cos \theta$

2. $u\cos \theta u\cos \alpha$

3. $\frac{u\sin \theta }{\sin \alpha }$

4. $\frac{u\cos \theta }{\cos \alpha }$

A particle is moving along the path y = ${\mathrm{x}}^2$ from x = 0 m to x = 2 m. Then the distance traveled by the particle is:

1.  4 m

2.  $\sqrt{20} \mathrm{m}$

3.  $>\sqrt{20} \mathrm{m}$

4.  $<\sqrt{20} \mathrm{m}$

Six particles situated at the corners of a regular hexagon of side \(a\) move at constant speed \(v\). Each particle maintains a direction towards the particle at the next. The time which the particles will take to meet each other is:
1. \(\frac{2 a}{v}~\text{sec}\)
2. \(\frac{a}{v}~\text{sec}\)
3. \(\frac{2 a}{3v}~\text{sec}\)
4. \(\frac{3 a}{v}~\text{sec}\)

A body is projected with velocity $20\sqrt{3}$ m/s with an angle of projection 60$°$ with horizontal. Calculate velocity on that point where body makes an angle 30$°$ with the horizontal.

1. 20 m/s

2. $\frac{20}{\sqrt{3}} m/s$

3. $10\sqrt{3} m/s$

4. 10 m/s

In a uniform circular motion, which of the following quantity is not constant

1. Angular momentum

2. Speed

3. Kinetic energy

4. Momentum

A particle is moving with veocity $\overrightarrow{\mathrm{v}}=\mathrm{k}(\mathrm{y}\hat{\mathrm{i}}+\mathrm{x}\hat{\mathrm{j}})$; where k is constant. The general equation for the path is:

1. $\mathrm{y}={\mathrm{x}}^2+\mathrm{constant}$

2. ${\mathrm{y}}^2={\mathrm{x}}^2+\mathrm{constant}$

3. $\mathrm{y}=\mathrm{x}+\mathrm{constant}$

4. xy=constant

A particle is projected with a velocity u making an angle $\mathrm{\theta }$ with the horizontal. At any instant, its velocity v is at right angles to its initial velocity u; then v is:

1.  ucos$\mathrm{\theta }$

2.  utan$\mathrm{\theta }$

3.  ucot$\mathrm{\theta }$

4.  usec$\mathrm{\theta }$