Mass of planet is frac{1}{9} of mass of earth and its radius is half that of earth. If a body weight

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7.Gravitation

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The mass of planet is $\frac{1}{9}$ of the mass of the earth and its radius is half that of the earth. If a body weight $9\,N$ on the earth. Its weight on the planet would be ........ $N$

A

$6$

B

$4.5$

C

$4$

D

$9$

Solution

$\mathrm{g}_{\mathrm{p}}=\frac{\mathrm{Gmp}}{\mathrm{Rp}^{2}} \quad \mathrm{g}_{\mathrm{p}}=\frac{4 \mathrm{Gme}}{8 \mathrm{Re}^{2}}$

$\mathrm{g}_{\mathrm{p}}=\frac{4}{9} \mathrm{g}, \mathrm{w}_{\mathrm{p}}=\mathrm{mg}_{\mathrm{p}}=\frac{4}{9} \mathrm{mg}$

$\mathrm{w}_{\mathrm{p}}=\frac{4}{9} \times 9 \mathrm{N}=4 \mathrm{N}$

$\mathrm{mg}=9 \mathrm{N}$

Standard 11

Physics

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