Q125 / 160 · TS EAMCET 2013 · Physics

A ball at rest is dropped from a height of 12 . It losses $25 \%$ of its kinetic energy on striking the ground and bounces back to a height ' $h$ '. Then value of ' $h$ ' is

  • A
    $3 \mathrm{~m}$
  • B
    $6 \mathrm{~m}$
  • Correct answer
    C
    $9 \mathrm{~m}$
  • D
    $12 \mathrm{~m}$

Solution

Energy of balls at rest, $K_1=m g h_1$ and $K_2=m g h_2$ percentage loss in $\mathrm{KE}=\frac{K_1-K_2}{K_1} \times 100$ $$ \begin{array}{rlrl} & & \frac{25}{100} & =\left(\frac{12-h^2}{12}\right) \\ \Rightarrow \quad & \frac{25 \times 12}{100} & =12-h_2 \\ \Rightarrow & h_2 & =12-3=9 \mathrm{~m} \end{array} $$

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

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