Question:
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m << M, body 'Q' will have a maximum speed equal to '2u' after collision.
Reason R : During elastic collision, the momentum and kinetic energy are both conserved.
In the light of the above statements, choose the most appropriate answer from the options given below :
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m << M, body 'Q' will have a maximum speed equal to '2u' after collision.
Reason R : During elastic collision, the momentum and kinetic energy are both conserved.
In the light of the above statements, choose the most appropriate answer from the options given below :
Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m << M, body 'Q' will have a maximum speed equal to '2u' after collision.
Reason R : During elastic collision, the momentum and kinetic energy are both conserved.
In the light of the above statements, choose the most appropriate answer from the options given below :
Show Hint
Use conservation of momentum and kinetic energy to get \(v_Q = \frac{2Mu}{M+m}\), then take \(m \ll M\).
Updated On: Nov 4, 2026
- A is correct but R is not correct.
- A is not correct but R is correct.
- Both A and R are correct and R is the correct explanation of A.
- Both A and R are correct but R is NOT the correct explanation of A.
Show Solution
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The Correct Option is C
Solution and Explanation
In a head-on elastic collision, momentum and kinetic energy are both conserved, so R is correct.
Momentum: \(Mu = Mv_P + mv_Q\). Energy: \(\frac{1}{2}Mu^2 = \frac{1}{2}Mv_P^2+\frac{1}{2}mv_Q^2\).
Solving gives \(v_Q = \frac{2M}{M+m}u\).
For \(m \ll M\), \(v_Q \approx 2u\), the maximum possible speed of Q. So A is correct, and it follows from the conservation laws in R.
Answer: (3) Both A and R are correct and R is the correct explanation of A.
Momentum: \(Mu = Mv_P + mv_Q\). Energy: \(\frac{1}{2}Mu^2 = \frac{1}{2}Mv_P^2+\frac{1}{2}mv_Q^2\).
Solving gives \(v_Q = \frac{2M}{M+m}u\).
For \(m \ll M\), \(v_Q \approx 2u\), the maximum possible speed of Q. So A is correct, and it follows from the conservation laws in R.
Answer: (3) Both A and R are correct and R is the correct explanation of A.
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