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Physics Question on Gravitational Potential Energy

A particle of mass 10 g10\, g is kept on the surface of a uniform sphere of mass 100 kg100\, kg and radius 10 cm10 \,cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere (you may take G=6.67×10−11Nm2/kg2G=6.67 \times 10^{-11} Nm ^{2} / kg ^{2} )

A

13.34×10−10J13.34\times 10^{-10}J

B

3.33×10−10J3.33\times 10^{-10}J

C

6.67 ×10−9J6.67\,\times 10^{-9}J

D

6.67 ×10−10J6.67\,\times 10^{-10}J

Answer

6.67 ×10−10J6.67\,\times 10^{-10}J

Explanation

Solution

Ui=−GMmr U_{i} =-\frac{G M m}{r} Ui=−6.67×10−11×100×10−20.1U_{i} =-\frac{6.67 \times 10^{-11} \times 100 \times 10^{-2}}{0.1} Ui=−6.67×10−110.1U_{i} =-\frac{6.67 \times 10^{-11}}{0.1} =−6.67×10−10J=-6.67 \times 10^{-10} J We know ∴W=ΔU\therefore W =\Delta U =Uf−Ul(∵Uf=0)=U_{f}-U_{l} \left(\because U_{f}=0\right) W=−Ui=6.67×10−10JW =-U_{i}=6.67 \times 10^{-10} J