A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is:

1. $\sqrt{u^2-2gL}$

2. $\sqrt{2gL}$

3. $\sqrt{u^2-gl}$

4. $\sqrt{2(u^2-gL)}$

The driver of a car travelling at velocity v suddenly sees a broad wall in front of him at a distance d. He should 

1. Brake sharply

2. Turn sharply

3. (1) and (2) both

4. None of the above

A 100 g iron ball having velocity 10 m/s collides with a wall at an angle 30° and rebounds with the same angle. If the period of contact between the ball and wall is 0.1 second, then the force experienced by the wall is 

1. 10 N

2. 100 N

3. 1.0 N

4. 0.1 N

A man fires a bullet of mass 200 g at a speed of 5 m/s. The gun is of one kg mass. By what velocity the gun rebounds backwards ?

1. 0.1 m/s

2. 10 m/s

3. 1 m/s

4. 0.01 m/s

A body of mass M at rest explodes into three pieces, two of which of mass M/4 each are thrown off in perpendicular directions with velocities of 3 m/s and 4 m/s respectively. The third piece will be thrown off with a velocity of 

1. 1.5 m/s

2. 2.0 m/s

3. 2.5 m/s

4. 3.0 m/s

Which of the following graph depicts spring constant k versus length l of the spring correctly

1.
2.
3.
4.

Work done by a frictional force is

1. Negative

2. Positive

3. Zero

4. All of the above

A block of mass 50 kg slides over a horizontal distance of 1 m. If the coefficient of friction between their surfaces is 0.2, then work done against friction is 

1. 98 J

2. 72J

3. 56 J

4. 34 J

A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is $\frac{m{v}^2}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle

(1) $\frac{m{v}^2}{\pi r^2}$

(2) Zero

(3) $\frac{m{v}^2}{r^2}$

(4) $\frac{\pi r^2}{m{v}^2}$

A man pushes a wall and fails to displace it. He does:
1. negative work
2. positive but not maximum work
3. no work at all
4. maximum work