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A stone thrown vertically upwards with a speed of $5 m/\text{sec}$ attains a height $H_{1}$. Another stone thrown upwards from the same point with a speed of $10 m/\text{sec}$ attains a height $H_{2}$. The correct relation between $H_{1}$ and $H_{2}$ is
Explanation
From third equation of motion $v^{2} = u^{2} + 2ah$ In first case initial velocity $u_{1} = 5 m/\text{sec}$ final velocity $v_{1} = 0$, $a = -g$ and max. height obtained is $H_{1}$, then, $H_{1} = 25/2g$ In second case $u_{2} = 10 m/\text{sec}$, $v_{2} = 0$, $a = -g$ and max. height is $H_{2}$ then, $H_{2} = 100/2g$. It implies that $H_{2} = 4H_{1}$