Question

A stone is projected at time t = 0 with a speed $v_0$ and an angle $\theta$ with the horizontal in a uniform gravitational field. The rate of work done (P) by the gravitational force plotted against time (t) will be as

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Rate of work done is the power associated with the force. It means rate of work done by the gravitational force is the power associated with the gravitational force. Gravitational force acting on the block is equal to its weight mg which acts vertically downwards.
Velocity of the particle (at time t) has two components,
(i) a horizontal component v cos $\theta$ and
(ii) a vertically upward component $(vsin\theta -gt)$
Hence, the power associated with the weight mg will be equal to $p=m\overrightarrow{g}.\overrightarrow{v}=-mg(vsin\theta -gt)$
This shows that the curve between power & time will be straight line having positive slope but negative intercept on Y-axis.
Hence (D) is correct.