If force $F=500-100t,$ then the function of impulse with time will be:
1. $500 t-50 t^2$
2. $50 t-10$
3. $50-t^2$
4. $100 t^2$
 

A particle of mass m is tied to a string of length $l$ and whirled into a horizontal plane. If the tension in the string is T, then the speed of the particle will be:

1. $\sqrt{\frac{Tl}{m}}$

2. $\sqrt{\frac{2Tl}{m}}$

3. $\sqrt{\frac{3Tl}{m}}$

4. $\sqrt{\frac{T}{ml}}$

A small ball is suspended from a thread. If it is lifted up with an acceleration of $4.9$ ms^–2 and lowered with an acceleration of $4.9$ ms^–2, then the ratio of the tension in the thread in both cases will be:
1. $1:3$
2. $3:1$
3. $1:1$
4. $1:5$

If a ladder is not in a balanced condition against a smooth vertical wall, then it can be brought to a balanced condition by:

For rocket propulsion, the velocity of exhaust gases relative to the rocket is $2$ km/s. If the mass of a rocket system is $1000$ kg, then the rate of fuel consumption for the rocket to rise with an acceleration $4.9$ m/s² will be:
1. $12.25~\text{kg}/\text{s}$
2. $17.5~\text{kg}/\text{s}$
3. $7.35~\text{kg}/\text{s}$
4. $5.2~\text{kg}/\text{s}$ 

A rigid rod is placed against the wall as shown in the figure. When the velocity at its lower end is $10$ ms^-1 and its base makes an angle $\alpha=60^\circ$ with horizontal, then the vertical velocity of its end $\mathrm{B}$ (in ms^-1) will be:
                  

If $100$ N force is applied to $10$ kg block as shown in diagram, then the acceleration produced for the slab will be:

Two masses as shown are suspended from a massless pulley. What would be the acceleration of the system when masses are left free?

1. $2g/3$
2. $g/3$
3. $g/9$
4. $g/7$
(where $g$ is the acceleration due to gravity.)

A body of mass 3 kg hits a wall at an angle of 60º & returns at the same angle. The impact time was 0.2 s. Calculate the force exerted on the wall.
       

1. 150 $\sqrt{3}$ N

2. 50 $\sqrt{3}$ N

3. 100 N

4. 75 $\sqrt{3}$ N

A mass of 1 kg is thrown up with a velocity of 100 m/s. After 5 seconds, it explodes into two parts. One part of mass 400 g comes down with a velocity of 25 m/s. Calculate the velocity of the other part.

1. 40 m/s upward

2. 40 m/s downward

3. 100 m/s upward

4. 60 m/s downward