The escape velocity of a body on an imagin

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The escape velocity of a body on an imaginary planet which is thrice the radius of the earth and double the mass of the earth is $({v_e}$ is the escape velocity of earth)

A

$\sqrt {2/3} \,{v_e}$

B

$\sqrt {3/2} \,{v_e}$

C

$\sqrt 2 /3\,{v_e}$

D

$2/\sqrt 3 \,{v_e}$

The escape velocity of a body on an imaginary planet which is thrice the radius of the earth and double the mass of the earth is $({v_e}$ is the escape velocity of earth)

$\frac{{{v_p}}}{{{v_e}}} = \sqrt {\frac{{{M_p}}}{{{M_e}}} \times \frac{{{R_e}}}{{{R_p}}}} = \sqrt {2 \times \frac{1}{3}} = \sqrt {\frac{2}{3}} $

${v_p} = \sqrt {\frac{2}{3}} {v_e}$