Work Energy and Power - Result Question 22
25. If the kinetic energy of a particle is increased by $300 %$, the momentum of the particle will increase by
[2002]
(a) $20 %$
(b) $200 %$
(c) $100 %$
(d) $50 %$
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Answer:
Correct Answer: 25. (c)
Solution:
- (c) New K.E., $E^{\prime}=E+3 E=4 E$
$p=\sqrt{2 m E}$ and $p^{\prime}=\sqrt{2 m E^{\prime}}$
$\frac{p^{\prime}}{p}=\sqrt{\frac{2 m \times 4 E}{2 m E}}=2$
$ \begin{aligned} & \frac{p^{\prime}}{p}-1=2-1 \text{ [on substrating } 1 \text{ in both sides.] } \\ & \frac{p^{\prime}-p}{p} \times 100=(2-1) \times 100=100 % \end{aligned} $
