Question

A particle is projected with a velocity 'u' making an angle ${}^{\prime }{\theta }^{\prime }$ with horizontal. The instantaneous power of gravitational force

• A. varies linearly with time
• B. is constant throughout the path
• C. is negative for complete path
• D. varies inversely with time

Answer 1

Answer: (A)

varies linearly with time

We know that the power P=$\overrightarrow{F}.\overrightarrow{v}$

Here, $F=-mg\hat{j}$

Also, $\overrightarrow{v}=$ $(u\cos \theta \hat{i}+(u\sin \theta -gt\left)\hat{j}\right)$

$P=-mg\hat{j}.$ ($(u\cos \theta \hat{i}+(u\sin \theta -gt\left)\hat{j}\right)$

$P=-mg(u\sin \theta -gt)$

Therefore it varies linearly with time.

Hence Option A is correct