A body of mass m hangs at one end of a string of length l, the other end of which is fixed. It is given a horizontal velocity so that the string would just reach where it makes an angle of 60° with the vertical. The tension in the string at mean position is 

1. 2 mg

2. mg

3. 3 mg

4. $\sqrt{3}mg$

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 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

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

1.
2.
3.
4.

A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by $x=3t-4t^2+t^3$, where x is in metres and t is in seconds. The work done during the first 4 seconds is 

(1) 5.28 J

(2) 450 mJ

(3) 490 mJ

(4) 530 mJ

A uniform chain of length 2m is kept on a table such that a length of 60cm hangs freely from the edge of the table. The total mass of the chain is 4kg. What is the work done in pulling the entire chain on the table?

(1) 7.2 J

(2) 3.6 J

(3) 120 J

(4) 1200 J

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that 

(1) Its velocity is constant

(2) Its acceleration is constant

(3) Its kinetic energy is constant

(4) It moves in a straight line

Two bodies of masses 1 kg and 5 kg are dropped gently from the top of a tower. At a point 20 cm from the ground, both the bodies will have the same 

(1) Momentum

(2) Kinetic energy

(3) Velocity

(4) Total energy

A cord is used to lower vertically a block of mass M by a distance d with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is 

(1) $Mg\frac{d}{4}$

(2) $3Mg\frac{d}{4}$

(3) $-3Mg\frac{d}{4}$

(4) Mgd 

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to- 

(1) x²

(2) e^x

(3) x

(4) log_e x