Mean radius of earth's orbit round sun is 1.5 × 10^{11}. mean radius of orbit of merc

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7.Gravitation

hard

The mean radius of the earth's orbit round the sun is $1.5 \times 10^{11}.$ The mean radius of the orbit of mercury round the sun is $6 \times10^{10}\,m.$ The mercury will rotate around the sun in

A

A year

B

Nearly $4$ years

C

Nearly $\frac{1}{4}$ year

D

$2.5$ years

Solution

$\frac{T_{1}^{2}}{q_{1}^{3}}=\frac{T_{2}^{2}}{r_{2}^{3}}$

$\frac{1}{\left(1 \cdot 5 \times 10^{11}\right)^{3}}=\frac{T_{2}^{2}}{\left(6 \times 10^{10}\right)^{3}}$

$T_{2}=\sqrt{\left(\frac{6 \times 10^{10}}{1.5 \times 10^{11}}\right)^{3}}$

$=\frac{\sqrt{\left(\frac{4}{10}\right)^{3}}}{\sqrt{\frac{64}{1000}}}$

$=\frac{8}{10 \sqrt{10}}$

$=\frac{0.8}{3.14}$

$\simeq 0.25$

Standard 11

Physics

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