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

A plumb line is suspended from the ceiling of a car moving with horizontal acceleration of \(a\). What will be the angle of inclination with the vertical:

1. \(\tan^{–1}(a/g)\)
2. \(\tan^{–1}(g/a)\)
3. \(\cos{–1}(a/g)\)
4. \(\cos^{–1}(g/a)\)

A body of mass \(2\ \text{kg}\) has an initial velocity of \(3\) meters per second along \(OE\) and it is subjected to a force of \(4\ \text{N}\) in a direction perpendicular to \(OE\). The distance of the body from \(O\) after \(4\) seconds will be:

1. \(12\ \text{m}\)
2. \(20\ \text{m}\)
3. \(8\ \text{m}\)
4. \(48\ \text{m}\)

A block of mass \(m\) is placed on a smooth wedge of inclination \(θ\). The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block will be: 

1. \(mg\cos 𝜃\)
2. \(mg\sin 𝜃\)
3. \(mg\)
4. \(\dfrac{mg}{\cos 𝜃}\)

The linear momentum \(p\) of a body moving in one dimension varies with time according to the equation \(p = a + bt^2\) where \(a\) and \(b\) are positive constants. The net force acting on the body is:

1. A constant
2. Proportional to \(t^2\)
3. Inversely proportional to \(t\)
4. Proportional to \(t\)

A man of mass \(80\ \text{kg}\) is standing in an elevator that is moving with an acceleration of \(6\ \text{m/s}^2\) in the upward direction. The apparent weight of the man will be \((\text{Take} \ g = 10\ \text{m/s}^2)\):

1. \(1480\ \text{N}\)
2. \(1280\ \text{N}\)
3. \(1380\ \text{N}\)
4. None of these

\(N\) bullets, each of mass \(m\ \text{kg}\) are fired with a velocity \(v\ \text{ms}^{–1}\) at the rate of \(n\) bullets per second upon a wall. The reaction offered by the wall on the bullets is given by:

1. \(nmv\)

2. \(\dfrac{Nmv}n\)$\frac{}{}$

3. \(n\dfrac{Nm}v\)$$

4. \(n\dfrac{Nv}m\)$$

A fireman slides down a rope whose maximum sustainable tension is \(\dfrac 23\) of his weight. The minimum downward acceleration required to prevent the rope from breaking is:

1. \(\dfrac 23 g\)

2. \(g\)

3. \(\dfrac 13 g\)

4. Zero