Q162 / 170 · Manipal (MET) 2017 · Physics

The linear momentum is increased by $50 \%$, the kinetic energy will increase by

  • A
    $50 \%$
  • B
    100%
  • Correct answer
    C
    125%
  • D
    25%

Solution

Let $p_1=p, p_2=p_1+50 \%$ of $p_1$ $=p_1+\frac{p_1}{2}=\frac{3 p_1}{2}$ $E \propto p^2$ $\Rightarrow \frac{E_2}{E_1}=\left(\frac{p_2}{p_1}\right)^2=\left(\frac{3 p_1 / 2}{p_1}\right)^2=\frac{9}{4}$ $\Rightarrow E_2=2.25 E_1=E_1+1.25 E_1$ $i e$, kinetic energy will increase by $125 \%$

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

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