Question

A raindrop of radius r falls from a certain height h above the ground. the work done by the gravitationl force is proportional to

(a) r

(b) r2

(c) r3

(d) r4

Answer 1

the work done by the gravitation force is proposional to r to the power 3

Answer 2

Answer:

The work done by the gravitational force is proportional to r³.

Therefore, the option (c) is correct.

Explanation:

We know that the work done by an object is the energy transferred due to the action of force.

Work = force × displacement

W = (ma) × displacement

Now when the work is done against the gravity, the force will be F = mg and the displacement will be 'h'.

So, work done, W = mgh                                              ................(1)

We know density = mass/volume

Mass of raindrop, $m=\rho *V$                                           ..............(2)

The volume of the raindrop, $V=\frac{4}{3}\pi r^{3}$

Substitute the value of volume 'V' in equation (2);

Mass, $m=\frac{4}{3} \pi r^{3}\rho$

Now put the value of mass(m) in equation (1);

$W=\frac{4}{3} \pi r^{3}\rho h$

W ∝ r³

Therefore, the work done by gravitational force is proportional to cube of radius of the raindrop (r³).