If a new planet is discovered rotating around Sun with orbital radius double that of earth, then wha

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7.Gravitation

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If a new planet is discovered rotating around Sun with the orbital radius double that of earth, then what will be its time period (in earth's days)

A

$ 1032$

B

$1023$

C

$1024$

D

$1043$

Solution

(a) ${T^2} \propto {R^3}$

${\left( {\frac{{{T_P}}}{{{T_E}}}} \right)^2} = {\left( {\frac{{{R_P}}}{{{R_E}}}} \right)^3} = {\left( {\frac{{2{R_E}}}{{{R_E}}}} \right)^3}$

$\frac{{{T_P}}}{{{T_E}}} = {(2)^{3/2}} = 2\sqrt 2 $

${T_P} = 2\sqrt 2 \times 365 = 1032.37= 1032$ days

Standard 11

Physics

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