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What is the amount of work done in moving mass m0 from surface to the center of solid ball?

Option: 1

\frac{-GMM_0}{R}


Option: 2

\frac{-2GMM_0}{R}


Option: 3

\frac{-3GMM_0}{2R}


Option: 4

\frac{-GMM_0}{2R}


Answers (1)

best_answer

As we learn

Gravitational Potential Energy at centre of earth relative to infinity -

U=m\left ( -\frac{3}{2}\frac{GM}{R} \right )

m\rightarrow mass of body

M\rightarrow Mass of earth

- wherein

{Ucentre=mVcentre}\\ {Vcentre\rightarrow Potential\: at\: centre}

 

 work done = m_{0}[v_{f}-v_{i}]

potential at surface = \frac{-GM}{R}

potential at inside point = \frac{-GM}{2R^{3}}[3R^{2}-r^{2}]

At center r = 0

v_{f} = \frac{-3}{2}\frac{GM}{R}

Workdone   = m_{0} [\frac{-3}{2}\frac{GM}{R} - (\frac{-GM}{R})]

w = \frac{-GMm_{0}}{2R}

 

Posted by

Deependra Verma

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