SATHEE: Work Energy and Power - Result Question 24

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) $1 : 1$

(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: $p_{1} = p_{2}$ ]

$\frac{m_{2}}{m_{1}} = \frac{4 \times p_{2}^{2}}{1 \times p_{1}^{2}} = \frac{4}{1} \times 1 \Rightarrow \frac{m_{1}}{m_{2}} = \frac{1}{4}$

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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

Answer:

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27. Two bodies with kinetic energies in the ratio $4 : 1$ are moving with equal linear momentum. The ratio of their masses is