The kinetic energy k of a particle moving along a circle of radius R depends on the distance covered s as k = as² where a is a constant. The force acting on the particle is 

(1) $2a\frac{s^2}{R}$

(2) $2as{\left(1+\frac{{\displaystyle s^2}}{{\displaystyle R^2}}\right)}^{1/2}$

(3) 2 as

(4) $2a\frac{R^2}{s}$

A stone of mass 1 kg tied to a light inextensible string of length $L=\frac{10}{3}m$ is whirling in a circular path of radius L in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be 10 m/sec², the speed of the stone at the highest point of the circle is 

(1) 20 m/sec

(2) $10\sqrt{3}m/\sec$

(3) $5\sqrt{2}m/\sec$

(4) 10 m/sec

A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in:

(1)
(2)
(3)
(4)	Same in all cases

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