Gravitation Ques 1
1. The work done to raise a mass $\mathrm{m}$ from the surface of the earth to a height $h$, which is equal to the radius of the earth, is :
[2019]
(a) $\mathrm{mgR}$
(b) $2 $ $\mathrm{mgR}$
(c) $\frac{1}{2} $ $\mathrm{mgR}$
(d) $\frac{3}{2} $ $\mathrm{mgR}$
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Answer:
Correct Answer: 1.(c)
Solution: (c) Mass to be raised = $m$
Potential energy at the surface of the earth
$ U_{\text {surface }}=\frac{-G M m}{R} $
Potential energy at a height from the surface of the earth $h=\mathrm{R}$
$ U_{\text {height }}=\frac{-G M m}{2 R} $
According to work-energy theorem, work done $=$ change in $\mathrm{PE}$
$ \begin{aligned} & \therefore \mathrm{W}=\mathrm{U} _{\text {height }}-\mathrm{U} _{\text {surface }} \\ & \Rightarrow \frac{-G M m}{2 R}-\left(-\frac{G M m}{R}\right) \\ & =\frac{G M m}{2 R}=\frac{g R^2 m}{2 R}=\frac{m g R}{2} \quad \left(\because \mathrm{GM}=\mathrm{gR}^2\right) \end{aligned} $
BETA
