For a rocket moving in free space, the fraction of mass to be disposed of Off to attain a speed equal to two times the exhaust speed is given by (given ${\mathrm{e}}^2$ = 7.4)

1. 0.40

2.  0.37

3.  0.50

4.  0.86

A simple pendulum hangs from the roof of a train moving on horizontal rails. If the string is inclined towards the front of the train, then train is-

1. Moving with constant velocity

2. In accelerated motion

3. In retarded motion

4. At rest

The value of \(M\) of the hanging block is in the figure, which will prevent the smaller block (\(m\)\(=\)\(1\) kg) from slipping over the triangular block. All the surfaces are smooth and string and pulley are ideal. (Given: \(M'\)\(=4\) kg and \(\theta\) \(=37^\circ\))

           
1. \(12\) kg
2. \(15\) kg
3. \(10\) kg
4. \(4\) kg

A lighter body and heavier body both are moving with same momentum and applied same retarding force. Their stoping distances are $s_1 and s_2$ respectively. Then the correct relation between $s_1 and s_2$-

1. $s_1>s_2$

2. $s_1<s_2$

3. $s_1=s_2$

4. None of these

Let $\theta$ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of bob is m, the tension in the string is mgcos$\theta$-

1.  always 

2.  never

3.  at extreme

4.  at mean position

The graph for stopping time (t) versus mass (m) is shown in the figure. Then which one of the pairs is given?

1.  Momentum, force

2.  K.E., force

3.  Velocity, force

4.  None of these

A metal ring of mass m and radius R is placed on smooth horizontal table and is set rotating about its own axis in such a way that each part of the ring moves with a speed v. Tension in the ring is:

1. $\frac{m{v}^2}{R}$

2. $\frac{m{v}^2}{2R}$

3. $\frac{m{v}^2}{2\mathrm{\pi }R}$

4. None of these

Tension on the string at point P is T. The graph for tension (T) versus x is shown in the figure. Then the string is:

1.  massless

2.  massfull

3.  tension on every point on the string is same when the string is having finite mass 4

4.  None of these