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 kmph in still water. The river flows at 6 kmph. If he crosses the river from one bank to the other along the shortest possible path, time taken to cross the river of width 1 km is:

1. 1/8 h

2. 1/4 h

3. 1/2 h

4. 1 h

A bus is going to the North at a speed of 30 kmph. It makes a 90° 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.  $\frac{\mathrm{l}}{\mathrm{v} + \mathrm{u}}$

A spotlight (source) is fixed 4 m from the vertical wall and is rotating at rate 1 rad/s. The spot (image) moves horizontally on the wall. The speed of the spot on the wall, when the spotlight makes the angle of 45° with the wall, is (The line joining spot source and image is in the horizontal plane)

(1) 2 m/s

(2) 3 m/s

(3) 8 m/s

(4) 1 m/s

A projectile is projected from the ground such that 2 seconds before it reaches the highest point, its initial velocity makes an angle of 37° with vertical. Then the velocity of the projectile at the highest point is:

(1) 5 m/s

(2) 10 m/s

(3) 15 m/s

(4) 20 m/s

A ball is projected horizontally from the top of wall A of height 80 m with speed 10 m/s. At what distance from the wall ball hits the ground?

(1) 20 m

(2) 50 m

(3) 60 m

(4) 40 m