A machine gun is mounted on a \(2000\ \text{kg}\) car on a horizontal frictionless surface. At some instant, the gun fires bullets of mass \(10\ \text{g}\) with a velocity of \(500\ \text{m/s}\) with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is:

1. \(550\ \text{N}\)
2. \(50\ \text{N}\)
3. \(250\ \text{N}\)
4. \(250\ \text{dyn}\)

In the given diagram, the acceleration of the car will be:

1. \(0.25\ \text{m/s}^2\)
2. \(2.5\ \text{m/s}^2\)
3. \(5.0\ \text{m/s}^2\)
4. \(0.025\ \text{m/s}^2\)

A particle of mass \(0.3\ \text{kg}\) is subjected to a force \(F = –kx\) with \(k = 15\ \text{N/m}\). What will be its initial acceleration if it is released from a point \(20\ \text{cm}\) away from the origin:
1. \(5\ \text{m/s}^2\)
2. \(10\ \text{m/s}^2\)
3. \(3\ \text{m/s}^2\)
4. \(15\ \text{m/s}^2\)

An elevator weighing \(6000\ \text{kg}\) is pulled upward by a cable with an acceleration of \(5\ \text{ms}^{–2}\). Taking \(g\) to be \(10\ \text{ms}^{–2}\), the tension in the cable is:
1. \(6000\ \text{N}\)
2. \(9000\ \text{N}\)
3. \(60000\ \text{N}\)
4. \(90000\ \text{N}\)

The ratio of the weight of a man in a stationary lift to that when it is moving downward with uniform acceleration \(a\) is \(3 : 2\). The value of \(a\) is:

1. \(\dfrac 32 g\)

2. \(\dfrac g3\)$\frac{}{}$

3. \(\dfrac 23 g\)

4. \(g\)

If the force on a rocket having an exhaust velocity of \(300\ \text{m/s}\) is \(210\ \text{N}\), then the rate of combustion of the fuel is:

1. \(0.7\ \text{kg/s}\)
2. \(1.4\ \text{kg/s}\)
3. \(0.07\ \text{kg/s}\)
4. \(10.7\ \text{kg/s}\)

In an elevator moving vertically upward with an acceleration \(g\), the force exerted on the floor by a passenger of mass \(M\) is:

1. \(Mg\)

2. \(\dfrac 12 Mg\)

3. Zero

4. \(2 Mg\)

A \(5000\ \text{kg}\) rocket is set for vertical firing. The exhaust speed is \(800\ \text{ms}^{–1}\). To give an initial upward acceleration of \(20\ \text{ms}^{–2}\), the amount of gas ejected per second to supply the needed thrust will be: (Take \(g = 10\ \text{ms}^{–2}\)) 

1. \(127.5\ \text{kg s}^{–1}\)

2. \(187.5\ \text{kg s}^{–1}\)

3. \(185.5\ \text{kg s}^{–1}\)

4. \(137.5\ \text{kg s}^{–1}\)

If a person with a spring balance and a body hanging from it goes up and up in an aeroplane, then the reading of the weight of the body as indicated by the spring balance will:

1. Go on increasing
2. Go on decreasing
3. First increase and then decrease
4. Remain the same

A body is given motion from rest to move in a straight line. If an opposite force then obstructs it, then:

1. The body may necessarily change direction
2. The body is sure to slow down
3. The body will necessarily continue to move in the same direction at the same speed
4. None of these