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 up with an acceleration \(4.9\) m/s² will be:
1. \(12.25\) kg/s
2. \(17.5\) kg/s
3. \(7.35\) kg/s
4. \(5.2\) kg/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