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A particle of mass m is placed at a dist...

A particle of mass `m` is placed at a distance of `4R` from the centre of a huge uniform sphere of mass `M` and radius `R`. A spherical cavity of diameter `R` is made in the sphere as shown in the figure. If the gravitational interaction potential energy of the system of mass `m` and the remaining sphere after making the cavity is `(lambdaGMm)/(28R)`. Find the value of `lambda`

Text Solution

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`PE_("net")=PE_("due to entirc sphere")-PE_("due to removed portion")`
`PE_("net")=-(GMm)/(4R)-[(-GMm)/(4R-(R//2))]` but `M.=(M)/(8) ( :. M prop R^(3)) M.=(M//(4)/(3)piR^(3))(4)/(3)pi((R )/(2))^(3)=(M)/(8)`
`PE_("net")=-(6GMm)/(28R)`
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