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A projectile is fired from the surface of the earth with a velocity of $5 \mathrm{~ms}^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3 \mathrm{~ms}^{-1}$ at the same angle follows a trajectory while 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 $\mathrm{ms}^{-2}$ ) is: (given $\left.g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$
Option A $\quad 3.5$
Option B $\quad 5.9$
Option C $\quad 16.8$
Option D $\quad 110.8$

The correct Option is A

As we know range is given as $\frac{u^{2} \sin 2 \theta}{g}$ so $g \infty u^{2}$

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