# A particle of mass 10 g is kept on the surface of  a uniform sphere of mass 100 Kg  and radius  10 cm  Find the work to be done against the gravitational force between them to take the particle far away from the sphere.( Option 1) Option 2) Option 3) Option 4)

As we learnt in

Change of potential energy -

$\Delta U=GMm\left [ \frac{1}{r_{1}}-\frac{1}{r_{2}} \right ]$

$r_{1}>r_{2}$

$\Delta U\rightarrow$ change of energy

$r_{1},r_{2}\rightarrow$ distances

- wherein

if body is moved from  $r_{1}$ to $r_{2}$  use this equation

dw=$\int dr=\frac{Gm_{1}m_{2}}{r^{2}} dr$

$\int dw=Gm_{1}m_{2}\int_{r}^{\infty }\frac{dr}{r^{2}}=Gm_{1}m_{2}\left [ \frac{1}{r} \right ]^\infty _r$

W=$\frac{Gm_{1}m_{2}}{r}$

W=$\frac{\left ( 6.67\times10 ^{-11} \right )\left ( 100\times \right )\left ( 10\times 10^{-3} \right )}{10\times 10^{-2}}$

=$6.67\times 10^{-10}J$

Option 1)

Incorrect Option

Option 2)

Correct option

Option 3)

Incorrect Option

Option 4)

Incorrect Option

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