Question

A particle of mass $m$ is projected at an angle $\alpha $ to the horizontal with an initial velocity $u$ . The work done by gravity during the time it reaches its highest point is -

• A. $\text{mu}^{2} \text{sin}^{2} \alpha $
• B. $\frac{m u^{2} c o s^{2} \alpha }{2}$
• C. $\frac{m u^{2} s i n^{2} \alpha }{2}$
• D. $-\frac{m u^{2} s i n^{2} \alpha }{2}$

Answer 1

Answer: (D)

$\text{W}_{\text{g}} = - \Delta \text{U}$
Work done by gravity = decrease in potential energy
$\mathrm{W}=-\mathrm{mgH}=-\mathrm{mg}\left(\frac{\mathrm{u}^2 \sin ^2 \alpha}{2 \mathrm{~g}}\right)$
$= \, -\frac{m u^{2} s i n^{2} \alpha }{2}$