The escape velocity for a rocket from eart

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The escape velocity for a rocket from earth is $11.2\, km/sec.$ Its value on a planet where acceleration due to gravity is double that on the earth and diameter of the planet is twice that of earth will be in .........  $km/sec$

A

$11.2$

B

$5.6$

C

$22.4$

D

$53.6$

The escape velocity for a rocket from earth is $11.2\, km/sec.$ Its value on a planet where acceleration due to gravity is double that on the earth and diameter of the planet is twice that of earth will be in .........  $km/sec$

$\frac{{{v_p}}}{{{v_e}}} = \sqrt {\frac{{{g_p}}}{{{g_e}}} \times \frac{{{R_p}}}{{{R_e}}}} $= $\sqrt {2 \times 2} = 2$ 

$⇒$ ${v_p} = 2 \times {v_e} = 2 \times 11.2 = 22.4\;km/s$