A projectile is fired from surface of earth with a velocity of 5, ms^{-1} and angle θ with horizont

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7.Gravitation

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A projectile is fired from the surface of the earth with a velocity of $5\, ms^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3\, ms^{-1}$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $ms^{-2}$) is (given $g = 9.8\, m/s^2$)

A

$3.5$

B

$5.9$

C

$16.3$

D

$110.8$

Solution

As Range $=\frac{u^{2} \sin 2 \theta}{g}$ so $g \propto u^{2}$

Therefore $g_{\text {planet }}=\left(\frac{3}{5}\right)^{2}\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right)=3.5 \mathrm{m} / \mathrm{s}^{2}$

Standard 11

Physics

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