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 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. \(\dfrac {2}{\sqrt5T} \)

If the rope of the lift breaks suddenly, the tension exerted by the surface of the lift \((a = \text{acceleration of lift})\):

1. \(mg\)
2. \(m(g + a)\)
3. \(m(g – a)\)
4. \(0\)

A lift of mass \(1000\ \text{kg}\) is moving with an acceleration of \(1\ \text{m/s}^2\) in the upward direction. The tension developed in the string, which is connected to the lift, is:

1. \(9,800\ \text{N}\)

2.  \(10,000\ \text{N}\)

3. \(10,800\ \text{N}\)

4.  \(11,000\ \text{N}\)

A lift is accelerating vertically downward with acceleration (\(a\)). A man inside the lift moves a ball upward with acceleration \(a_0\) relative to the lift, where \( (a_0 < a)\). What is the acceleration of the ball as observed by a stationary observer on the ground?

1. \((a + a_0)\) upward

2. \((a - a_0)\) upward

3. \((a + a_0)\) downward

4. \((a - a_0)\) downward

A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The accelerations of the ball as observed by the man in the lift and a man standing stationary on the ground are, respectively:

1. \(g, g\)
2. \(g- a, g - a\)
3. \(g- a , g\)
4. \(a, g\)