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 \(m_1\) and \(m_2\) 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 the masses are pushed apart. The mass \(m_1\) travels a distance \(s_1\) and stops. If the coefficients of friction between the balls and the ground are the same, the mass \(m_2\) stops after travelling the distance:

1. \(s_2=\dfrac{m_1}{m_2}s_1\)

2. \(s_2=\dfrac{m_2}{m_1}s_1\)

3. \(s_2=\dfrac{(m_1)^2}{(m_2)^2}s_1\)

4. \(s_2=\dfrac{(m_2)^2}{(m_1)^2}s_1\)

A force vector applied to a mass is represented as \(\vec F=6\hat i−8\hat j+10\hat k\) and accelerates it with \(1\ \text{m/s}^2\). The mass of the body will be:

1. \(10\sqrt 2\ \text{kg}\)
2. \(2\sqrt {10}\ \text{kg}\)$\mathrm{}$
3. \(10\ \text{kg}\)
4. \(20\ \text{kg}\)

A cricket ball of mass \(250\ \text{g}\) collides with a bat with velocity \(10\ \text{m/s}\) and returns with the same velocity within \(0.01\) second. The average force acted on the bat is:

1. \(25\ \text{N}\)
2. \(50\ \text{N}\)
3. \(250\ \text{N}\)
4. \(500\ \text{N}\)

A pendulum bob of mass \(50\ \text{g}\) is suspended from the ceiling of an elevator. The tension in the string if the elevator goes up with uniform velocity is approximately:

1. \(0.30\ \text{N}\)
2. \(0.40\ \text{N}\)
3. \(0.42\ \text{N}\)
4. \(0.50\ \text{N}\)

The average force necessary to stop a bullet of mass 20 g moving with a speed of 250 m/s, as it penetrates into the wood for a distance of 12 cm is 

1. 2.2 × 10³ N

2. 3.2 × 10³ N

3. 4.2 × 10³ N

4. 5.2 × 10³ N

A man measures the time period of a pendulum \((T)\) in a stationary lift. If the lift moves upward with acceleration \(\dfrac g4\) then the new time period will be:

1. \(\dfrac {2T} {\sqrt5}\)

2. \(\dfrac {\sqrt5T} {2}\)

3. \(\dfrac {\sqrt5} {2T}\)

4. \(\dfrac {2}{\sqrt5T} \)