A body is thrown upwards from the earth surface with velocity $5 {ms}^{- 1}$ and from a planet surface with velocity ${3ms}^{- 1}$ . Both follow the same path. What is the projectile acceleration due to gravity on the planet ? Acceleration due to gravity on earth is $10 {ms}^{- 2}$ .

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$4 {ms}^{- 2}$

$3.6 {ms}^{- 2}$

$2 {ms}^{- 2}$

$5 {ms}^{- 2}$

answer is B.

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Detailed Solution

Let $g'$ be the acceleration due to gravity on the planet. As per question, horizontal range is same,

so $\frac{u_{1}^{2} \sin 2 θ}{g} = \frac{u_{2}^{2} \sin 2 θ}{g'} o r \frac{u_{1}^{2}}{g} = \frac{u_{2}^{2}}{g'}$

or $g' = \frac{u_{2}^{2}}{u_{1}^{2}} g = \frac{3^{2}}{5^{2}} \times 10 = 3.6 {ms}^{- 2}$ .

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