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 ball rolls off the top of a staircase with a horizontal velocity \(u\) m/s. If the steps are \(h\) metre high and \(b\) metre wide, the ball will just hit the edge of \(n^{th}\) 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 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 \(𝜃  \) with the horizontal with an initial speed \(u\). When it makes an angle \(𝛼\) with the horizontal, its speed \(v\) is:
1. \(𝑢 \cos 𝜃\)

2. \(𝑢 \cos 𝜃 \ 𝑢 \cos 𝛼 \)

3. \(\dfrac{u\sin \theta}{\sin \alpha}\)

4. \(\dfrac{u\cos \theta}{\cos \alpha}\)

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.  $\sqrt{20}<mspace\; width="1em"></mspace>\mathrm{m}$

3.  $>\sqrt{20}<mspace\; width="1em"></mspace>\mathrm{m}$

4.  $<\sqrt{20}<mspace\; width="1em"></mspace>\mathrm{m}$

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. \(\dfrac{2 a}{v}\ \text{seconds}\)

2. \(\dfrac{a}{v}~\text{seconds}\)

3. \(\dfrac{2 a}{3v}~\text{seconds}\)

4. \(\dfrac{3 a}{v}~\text{seconds}\)

A body is projected with velocity \(20\sqrt3 \text{  m/s}\) with an angle of projection \(60^°\) with the horizontal. The velocity at the point where the body makes an angle \(30^°  \)with the horizontal is:

1. \(20 \text{  m/s}\)

2. \(\dfrac{20}{\sqrt3} \text{  m/s}\)

3. \(10\sqrt3 \text{  m/s}\)

4. \(10 \text{  m/s}\)

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 velocity \(\vec v=k(y\hat i+x \hat j)\), where \(k\) is constant. The general equation for the path is:

1. \(y=x^2+\text{constant}\)

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

3. \(y=x+\text{constant}\)$\mathrm{}$

4. \(xy=\text{constant}\)

A particle is projected with a velocity \(u\) making an angle \(θ\) with the horizontal. At any instant, its velocity \(v\) is at right angles to its initial velocity \(u\); then \(v\) is:

1.  \(u \cos \theta \)

2.  \(u \tan θ\)

3.  \( u \cot θ\)

4.  \(u \sec θ\)