Question

A particle is projected with a velocity $u$ making an angle $\theta$ with the horizontal. The instantaneous power of the gravitational force

• A. Varies linearly with time.
• B. Is constant throughout
• C. Is negative for complete path
• D. None of these

Answer 1

Answer: (A)

At any time, $\overrightarrow{v}=\left[\left(\text{u}\text{ cos}\theta \right)\hat{\text{i}}+\left(\text{u}\text{ sin}\theta -\text{gt}\right)\hat{\text{j}}\right]$
$\text{P}=\overrightarrow{F}\text{.}\overrightarrow{v}=\left(\text{-}\text{mg}\hat{\text{j}}\right)\text{.}\left[\text{u}\text{ cos}\theta \hat{\text{i}}+\left(\text{u}\text{ sin}\theta -\text{gt}\right)\hat{\text{j}}\right]$
$={\text{mg}}^2\text{t}-\text{mgu }\text{sin}\theta$
Hence, power varies linearly with time.