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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 $ms^{-2}$) (given g = 9.8 $ms^{-2}$)
A
3.5
B
5.9
C
16.3
D
110.8
Detailed Solution
Range $= \frac{u^2\sin2\theta}{g}$; for identical trajectories at the same angle, $g \propto u^2$.
$g_{planet} = \left(\frac{3}{5}\right)^2\times 9.8 = 3.5$ $ms^{-2}$
$g_{planet} = \left(\frac{3}{5}\right)^2\times 9.8 = 3.5$ $ms^{-2}$