If it is safe to jump from a height of $2 m$ on to the earth, what would be the safe height on a planet where the value of ' $g$ ' is $1.96 m s^{- 2}$ ?

2 m

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4 m

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6 m

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10 m

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Solution

The correct option is D $10 m$
Acceleration due to gravity on earth $g_{e a r t h} = 9.8 m / s^{2}$
Safe height on earth $H_{e a r t h} = 2 m$
Acceleration due to gravity on planet $g_{p l a n e t} = 1.96 m / s^{2}$
So, safe height on planet $H_{p l a n e t} = \frac{g_{e a r t h} H_{e a r t h}}{g_{p l a n e t}}$
$⟹ H_{p l a n e t} = \frac{9.8 \times 2}{1.96} = 10 m$

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