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Work Power and Energy question

2023 · 13 Apr · Shift 1 · Q63
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Work Power and Energy question

2023 · 13 Apr · Shift 1 · Q63

JEE MainPhysicsWork Power and EnergyMCQ+4 / −1
Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is :
  1. A
    3:43: 43:4
  2. B
    4:34: 34:3
  3. C
    9:169: 169:16
  4. D
    16:916: 916:9
View written solutionFree

Correct answer: C

  1. Use the relation between kinetic energy, momentum, and mass

For a body with linear momentum ppp and mass mmm,

K=p22mK = \frac{p^2}{2m}K=2mp2​

  1. Given same linear momentum

Since both bodies have the same momentum, ppp is constant for both. Therefore,

K∝1mK \propto \frac{1}{m}K∝m1​

So the ratio of kinetic energies is the inverse of the ratio of masses.

  1. Apply the given kinetic energy ratio

Given,

K1:K2=16:9K_1 : K_2 = 16 : 9K1​:K2​=16:9

Thus,

K1K2=m2m1=169\frac{K_1}{K_2} = \frac{m_2}{m_1} = \frac{16}{9}K2​K1​​=m1​m2​​=916​

So,

m1m2=916\frac{m_1}{m_2} = \frac{9}{16}m2​m1​​=169​

Hence,

m1:m2=9:16m_1 : m_2 = 9 : 16m1​:m2​=9:16

  1. Match with options

This corresponds to Option C.

Final Answer: 9:169:169:16

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