Q126 / 160 · AP EAMCET 2021 (25 Aug Shift 1) · Physics

Two bodies having masses in the ratio $2: 3$ fall freely under gravity from heights which are in the ratio $9: 16$. The ratio of their linear momenta on touching the ground is

  • A
    $2: 9$
  • B
    $3: 16$
  • Correct answer
    C
    $1: 2$
  • D
    $3: 2$

Solution

The velocity acquired by a mass $m$ falling freely under the influence of gravity from the heigh $h$ is $$ v=\sqrt{2 g h} $$ Momentum of first body, $p_1=m_1 v_1$ $$ \Rightarrow \quad=m_1 \sqrt{2 g h_1} $$ Momentum of second body $p_2=m_2 v_2$ $$ \Rightarrow \quad=m_2 \sqrt{2 g h_2} $$ The ratio of their linear momenta on touching the ground is $$ \begin{aligned} \frac{p_1}{p_2} & =\frac{m_1 \sqrt{2 g h_1}}{m_2 \sqrt{2 g h_2}} \\ & =\frac{2}{3} \times \sqrt{\frac{9}{16}}=\frac{2}{3} \times \frac{3}{4}=\frac{1}{2} \text { or } 1: 2 \end{aligned} $$

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

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