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. \(137.5\ \text{kg s}^{–1}\)

A person is carrying a spring balance with a body suspended from it inside an aeroplane. The aeroplane initially accelerates vertically upward and then continues ascending at a constant velocity to a very high altitude. Assuming the initial upward acceleration is sufficient to increase the reading, the reading of the spring balance:

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

Two balls of masses m₁ and m₂ are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly the powder charge explodes and masses are pushed apart. The mass m₁ travels a distance s₁ and stops. If the coefficients of friction between the balls and ground are same, the mass m₂ stops after travelling the distance 

1. $s_2=\frac{m_1}{m_2}{s}_1$

2. $s_2=\frac{m_2}{m_1}{s}_1$

3. $s_2=\frac{m_1^2}{m_2^2}{s}_1$

4. $s_2=\frac{m_2^2}{m_1^2}{s}_1$

A force vector applied on a mass is represented as $\overrightarrow{F}=6\hat{i}-8\hat{j}+10\hat{k}$ and accelerates with 1 m/s². What will be the mass of the body?

1. $10\sqrt{2}kg$

2. $2\sqrt{10}kg$

3. 10 kg

4. 20 kg