A body is executing uniform circular motion in a circle of radius 100 m at speed 10 m/s. Acceleration of the body is :

(1) Zero

(2) 2 $\mathrm{m}/{\mathrm{s}}^2$

(3) 1 $\mathrm{m}/{\mathrm{s}}^2$

(4) 5 $\mathrm{m}/{\mathrm{s}}^2$

A particle started revolving from rest with a constant angular acceleration $\alpha$ in a circular path of radius r. If centripetal acceleration becomes numerically equal to tangential acceleration at time t, then t is equal to:

1.  $\mathrm{t} = \frac{1}{\mathrm{\alpha }}$

2.  $\mathrm{t} = \frac{1}{{\mathrm{\alpha }}^2}$

3.  $\mathrm{t} = \frac{1}{\sqrt{\mathrm{\alpha }}}$

4.  $\mathrm{t} = \sqrt{\mathrm{\alpha }}$

Balls A and B are thrown simultaneously from two points lying on the same horizontal plane separated by a distance 120 m. Path of A w.rt. B is

(1) Parabola

(2) Hyperbola

(3) Circle

(4) Straight line

Which of the following is the angle between velocity and acceleration of a body in uniform circular motion?
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(90^\circ\)

A man wants to cross a river of width 500 m in the minimum distance. The rowing speed of man relative to water is 3 km/h and river flows with speed 2 km/h. The time taken by the man to cross the river

(1) 2$\sqrt{6}$ minute

(2) 6$\sqrt{3}$ minute

(3) 2$\sqrt{5}$ minute

(4) 6$\sqrt{5}$ minute

A person is rotating in a horizontal circle of radius 7 m. Find the period of rotation for which the acceleration is equal to 3g.

(1) 2.6 s

(2) 2.8 s

(3) 3.1 s

(4) 4.3 s

A man can row a boat with a speed of \(10~\text{kmph}\) in still water. The river flows at \(6~\text{kmph}.\) If he crosses the river from one bank to the other along the shortest possible path, the time taken to cross the river of width \(1~\text{km}\) is:
1. \(\frac{1}{8}~\text{hr}\)
2. \(\frac{1}{4}~\text{hr}\)
3. \(\frac{1}{2}~\text{hr}\)
4. \(1~\text{hr}\)

A bus is going to the North at a speed of \(30\) kmph. It makes a \(90^{\circ}\) left turn without changing the speed. The change in the velocity of the bus is:

Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)

A pilot is supposed to fly east from A to B and back again A due west. If the wind is blowing due south, find time for the round trip, if AB = l. The velocity of the plane in the air is v and the velocity of wind is u.

1.  $\frac{\mathrm{l}}{\sqrt{{\mathrm{v}}^2 + {\mathrm{u}}^2}}$

2.  $\frac{2\mathrm{l}}{\sqrt{{\mathrm{v}}^2 - {\mathrm{u}}^2}}$

3.  $\frac{\mathrm{l}}{\sqrt{{\mathrm{v}}^2 - {\mathrm{u}}^2}}$

4.  $\frac{\mathrm{l}}{\mathrm{v} + \mathrm{u}}$