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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.

( $\left ( You\: might\: take\: G= 6.67\times 10^{-11}Nm^{2}/kg^{2} \right )$

Option 1)
$6.67\times 10^{-9}J$

Option 2)
$6.67\times 10^{-10}J$

Option 3)
$13.34\times 10^{-10}J$

Option 4)
$3.33\times 10^{-10}J$

Answers (1)

best_answer

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)

$6.67\times 10^{-9}J$

Incorrect Option

Option 2)

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

Correct option

Option 3)

$13.34\times 10^{-10}J$

Incorrect Option

Option 4)

$3.33\times 10^{-10}J$

Incorrect Option

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prateek

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