A body of mass \(5~\text{kg}\) is acted upon by two perpendicular forces, \(8~\text N\) and \(6~\text N.\) The magnitude of the acceleration of the body is:
1. \(0.99~\text{ms}^{-2}\)
2. \(3~\text{ms}^{-2}\)
3. \(2~\text{ms}^{-2}\)
4. \(0.77~\text{ms}^{-2}\)

A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m/s, what is the recoil speed of the gun?
1. \(1.2 \mathrm{~cm} \mathrm{~s}^{-1}\)
2. \(2.2 \mathrm{~cm} \mathrm{~s}^{-1}\)
3. \(2.0 \mathrm{~cm} \mathrm{~s}^{-1}\)
4. \(1.6 \mathrm{~cm} \mathrm{~s}^{-1}\)

A trolley of mass \(300\) kg carrying a sandbag of \(25\) kg is moving uniformly with a speed of \(27\) km/h on a frictionless track. After a while, the sand starts leaking out of a hole on the floor of the trolley at the rate of \(0.05\) kgs^–1. What is the speed of the trolley after the entire sandbag is empty?

A bullet of mass 0.012 kg and horizontal speed $70<mspace\; width="1em"></mspace>m<mspace\; width="1em"></mspace>s^{-1}$ strikes a block of wood of mass 0.4 kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. The height to which the block rises is:

1. 11.2 cm
2. 12.7 cm
3. 28.5 cm
4. 21.2 cm

A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of $4<mspace\; width="1em"></mspace>{\mathrm{ms}}^{-1}$ relative to the trolley in a direction opposite to its motion, and jumps out of the trolley. What is the final speed of the trolley?

1. 1.01 m/s
2. 10.36 m/s
3. 9.64 m/s
4. 11.20 m/s