The rain drop of mass 1 g , starts with zero velocity from a height of 1 km . It hits the ground with a speed of $5 \mathrm{~m} / \mathrm{s}$. The work done by the unknown resistive force is $\_\_\_\_$ J.

(take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

Two blocks ( $P$ and $Q$ ) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pully which is fixed on the edge of a cube $(S)$, as shown in the figure below. Block $P$ is positioned on the top surface which has no friction and block $Q$ is in contact with side-surface, having coefficient friction $\mu$. The cube ( $S$ ) moves towards the right with acceleration of $\frac{g}{2}$, where $g$ is gravitational acceleration. During this movement the block $P$ and $Q$ remain stationary. The value of $\mu$ is $\_\_\_\_$ (take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^8 \mathrm{~N} / \mathrm{m}^2$ and its radius is 4 mm , then maximum acceleration the lift can take is $\_\_\_\_$ $\mathrm{m} / \mathrm{s}^2$.

(take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ and $\pi=3.14$ )

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm . It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are $\_\_\_\_$ and $\_\_\_\_$ respectively.