A person is pulling a mass m from ground on a rough hemispherical surface upto the top of the hemisphere with the help of a light inextensible string as shown in the figure. The radius of the hemisphere is R. The work done by the tension in the string is

mgR(1 + )

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mgR

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mgR(1-)

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mg(R/2).

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Solution

The correct option is A mgR(1 + )

Forces due to friction and gravity will be as shown in figure, apart from this tension force T and normal force will also be acting.
By work energy theorem ,
Work done by all forces = Change in K.E
$W_{m g} + W_{f r i c t i o n} + W_{T} = 0$
$- m g R -$ \int_{\theta=0}^{\theta=90} \mu mgsin\theta d\theta +W_{T}=0 $O n s o l v i n g,$ W-{T}=mgR(1+\mu)$

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