Q109 / 180 · JIPMER 2019 · Physics

If three objects are thrown with velocity $\sqrt{\frac{2 g H}{3}}, \sqrt{2 \mathrm{gH}}, \sqrt{\frac{g H}{3}}$, then find the ratio of their maximum heights.

  • Correct answer
    A
    $2: 6: 1$
  • B
    $2: 5: 3$
  • C
    $2: 4: 7$
  • D
    $3: 7: 4$

Solution

Maximum height of projectile $\mathrm{H}_{\max }=\frac{\mathrm{u}^2}{2 \mathrm{~g}}$ $\begin{aligned} & \therefore\left(\mathrm{H}_{\max }\right)_1:\left(\mathrm{H}_{\max }\right)_2:\left(\mathrm{H}_{\max }\right)_3 \\ &=\frac{\left(\sqrt{\frac{2 \mathrm{gH}}{3}}\right)^2}{2 \mathrm{~g}}: \frac{(\sqrt{2 \mathrm{gH}})^2}{2 \mathrm{~g}}: \frac{\sqrt{\frac{\mathrm{gH}}{3}}}{2 \mathrm{~g}}=\frac{2}{3}: 2: \frac{1}{3} \\ & \quad=2: 6: 1 \end{aligned}$

Hence, the correct answer is option: 'A'.

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