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. \(a, g\)

A monkey of mass 20kg is holding a vertical rope. The rope will not break when a mass of 25 kg is suspended from it but will break if the mass exceeds 25 kg. What is the maximum acceleration with which the monkey can climb up along the rope (g = 10 m/s²) 

1. 10 m/s²

2. 25 m/s²

3. 2.5 m/s²

4. 5 m/s²