Q126 / 160 · TS EAMCET 2024 (11 May Shift 1) · Physics

A body thrown vertically upwards from the ground reaches a maximum height ' $h$ '. The ratio of the kinetic and potential energies of the body at a height $40 \%$ of $h$ from the ground is

  • A
    $2: 3$
  • Correct answer
    B
    $3: 2$
  • C
    $1: 1$
  • D
    $4: 9$

Solution

In vertical upward projection, $\begin{aligned} & \text { At } \mathrm{y}=40 \% \text { of } \mathrm{h}=0.4 \mathrm{~h}, \\ & \mathrm{PE}=\mathrm{mgy}=\mathrm{mg}(0.4 \mathrm{~h})=0.4 \mathrm{mgh} \\ & \mathrm{KE}=\frac{1}{2} \mathrm{mv}^2=\frac{1}{2} \mathrm{~m}\left(\mathrm{u}^2-2 \mathrm{~g} \times 0.4 \mathrm{~h}\right) \\ & =\frac{1}{2} \mathrm{~m}(2 \mathrm{gh}-0.8 \mathrm{gh})=0.6 \mathrm{mgh} \\ & \therefore \frac{\mathrm{KE}}{\mathrm{PE}}=\frac{0.6 \mathrm{mgh}}{0.4 \mathrm{mgh}}=3: 2 \end{aligned}$

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

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