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Question

This question has statement I and Statement II. Of the four choices given after the Statements, choose the
one that best describes the two Statements.

Statement-I: A point particle of mass m moving with speed v collides with stationary point particle of mass
M. If the maximum energy loss possible is given as f(12mv2) then f=(mM+m).

Statement-II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

A
Statement-I is true, Statement-II is true, Statement-II is the correct explanation of Statement -I.
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B
Statement-I is false, Statement-II is true.
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C
Statement I is true, Statement-II is false.
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D
Statement-I is true, Statement-II is true, Statement-II is not the correct explanation of Statement.
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Solution

The correct option is B Statement-I is false, Statement-II is true.
The maximum Energy loss, E=p22m
where,
p = momentum,
m = the mass moving of the particle.

Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Maximum energy loss,

ΔE=P22mP22(m+M)

Where, (m+M)= resultant mass when the particle get stuck.

ΔE=P22m[1m(m+M)]
=P22m[M(m+M)]

Also, P=mv

ΔE=m2v22m[M(m+M)] =mv22[M(m+M)]

Comparing the expression withf(12mv2). Then,

f=Mm+M

Hence, Statement-I is wrong and statement-II is correct. So, the correct answer is (D).

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