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JIPMER 2019
Exam
JIPMER
Year
2019
Subject
Physics
Chapter
Motion in Two Dimensions

JIPMER 2019 · Physics · Motion in Two Dimensions

If three objects are thrown with velocity (2 g H)/(3) , 2 gH , (g...

If three objects are thrown with velocity 2gH3,2gH,gH3\sqrt{\frac{2 g H}{3}}, \sqrt{2 \mathrm{gH}}, \sqrt{\frac{g H}{3}}, then find the ratio of their maximum heights.

Options

  1. A2:6:12: 6: 1
  2. B2:5:32: 5: 3
  3. C2:4:72: 4: 7
  4. D3:7:43: 7: 4

Correct answer

A. 2:6:12: 6: 1

Step-by-step solution

Maximum height of projectile Hmax⁡=u22 g\mathrm{H}_{\max }=\frac{\mathrm{u}^2}{2 \mathrm{~g}}∴(Hmax⁡)1:(Hmax⁡)2:(Hmax⁡)3=(2gH3)22 g:(2gH)22 g:gH32 g=23:2:13=2:6:1\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}$$
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