1.

The work done to raise a mass m from the surfacof the earth to a height h, which is equal to thradius of the earth, is[NEET-2019](1) mgR.(2) 2mgR(3)1/2mgR(4)3/2mgR​

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AnswEr :

To FIND the work done in lifting an OBJECT of mass 'm' to a height 'H' which is equal to Earth' radius.

Initial Potential Energy in the object would be :

\sf U_o = - \dfrac{GMm}{R}

When the object is lifted to a height 'h' :

\sf U= - \dfrac{GMm}{R + h}

Here, h = radius of earth.

\longrightarrow \: \sf U = - \dfrac{GMm}{2R}

Now,

\implies\sf W= U - U_o \\ \\ \implies \sf \: W = \dfrac{GMm}{R} \big(1 - \dfrac{1}{2} ) \\ \\ \implies \sf \: W = \dfrac{GMm}{r}

Also,

\sf \: mg = \dfrac{GMm}{R {}^{2} } \\ \\ \longrightarrow \sf \: g {R}^{2} = GM

Thus,

\implies \sf \: W = \dfrac{ {mgR}^{2} }{2R} \\ \\ \implies \boxed{ \boxed{ \sf W = \dfrac{mgR}{2} }}

OPTION (C) is CORRECT


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