First slide

Work

Question

A uniform rod of mass $\sqrt{3}$ kg and length 2m is lying on a horizontal surface. It is raised until it makes an angle $30^{\circ}$ with vertical. The work done by gravity is ${(g=9.8ms}^{-2})$

Moderate

A

14.7 J
B

-14.7 J
C

8.49J
D

-8.49J

Solution

$\begin{array}{l} h = \frac{l}{2} \cos 30^{\circ} \\ h = \frac{2}{2} \times \frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{2} m \\ W = \vec{F} . \vec{S} = mg h cos 1 80 \end{array}$
$\begin{array}{l} W = \sqrt{3} \times 9.8 \times \frac{\sqrt{3}}{2} \times (- 1) \\ W = - 14.7 J \end{array}$

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