Work Energy and Power - Result Question 24
27. Two bodies with kinetic energies in the ratio $4: 1$ are moving with equal linear momentum. The ratio of their masses is
[1999]
(a) $1: 2$
(b) $1: 1$
(c) $4: 1$
(d) $1: 4$
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Answer:
Correct Answer: 27. (d)
Solution:
- (d) $\frac{(K . E)_1}{(K . E)_2}=\frac{\frac{1}{2} m_1 v_1^{2}}{\frac{1}{2} m_2 v_2^{2}}=\frac{4}{1} \Rightarrow \frac{m_1 v_1^{2}}{m_2 v_2^{2}}=\frac{4}{1}$
$\Rightarrow \frac{(m_1 v_1)^{2} m_2}{(m_2 v_2)^{2} m_1}=\frac{4}{1} \Rightarrow \frac{p_1^{2}}{p_2^{2}} \times \frac{m_2}{m_1}=\frac{4}{1}$
[Given: $p_1=p_2$ ]
$\frac{m_2}{m_1}=\frac{4 \times p_2^{2}}{1 \times p_1^{2}}=\frac{4}{1} \times 1 \Rightarrow \frac{m_1}{m_2}=\frac{1}{4}$
