An object with a mass \(10\ \text{kg}\) moves at a constant velocity of \(10\ \text{m/s}\). A constant force then acts for \(4\) seconds on the object and gives it a speed of \(2\ \text{m/s}\) in the opposite direction. The acceleration produced in it is:
1. \(3\ \text{m/s}^2\)
2. \(-3\ \text{m/s}^2\)
3. \(0.3\ \text{m/s}^2\)
4. \(-0.3\ \text{m/s}^2\)

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