The escape velocity of a body from the earth is $u$ . What is the escape velocity from a planet whose mass and radius are twice those of the earth?

2 u

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u

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4 u

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16 u

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Solution

The correct option is C $u$
Escape speed, $v_{e} = \sqrt{\frac{2 G M}{R}} = u$
For another planet both mass and radius are twice that of Earth.
$∴ v_{e}^{^{'}} = \sqrt{\frac{2 G \times 2 M}{2 R}}$
$\Rightarrow v_{e}^{^{'}} = \sqrt{\frac{2 G M}{R}} = u$

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The escape velocity of a body from the earth is u. What is the escape velocity from a planet whose mass and radius are twice those of the earth?

The correct option is C uEscape speed, ve=√2GMR=uFor another planet both mass and radius are twice that of Earth.∴v′e=√2G×2M2R⇒v′e=√2GMR=u

The escape velocity of a body from the earth is $u$ . What is the escape velocity from a planet whose mass and radius are twice those of the earth?

The correct option is C $u$
Escape speed, $v_{e} = \sqrt{\frac{2 G M}{R}} = u$
For another planet both mass and radius are twice that of Earth.
$∴ v_{e}^{^{'}} = \sqrt{\frac{2 G \times 2 M}{2 R}}$
$\Rightarrow v_{e}^{^{'}} = \sqrt{\frac{2 G M}{R}} = u$