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Byju's Answer

Standard VIII

Physics

Conservation of Momentum

Assertion A :...

Question

Assertion (A) : A body of mass " $m_{1}$ " collides elastically with another body of mass " $m_{2}$ " at rest the ratio of the the final energy of the first body to the final energy of the second body is $\frac{(m_{1} - m_{2})^{2}}{4 m_{1} m_{2}}$ .
Reason (R) : The collision is perfectly elastic and the coefficient of restitution is 1.

Both Assertion (A) and Reason (R) are correct and R is the correct explanation.

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Both Assertion (A) and Reason (R) are correct but the reason does not give the correct explanation.

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A is true but R is false.

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A is false but R is true.

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Solution

The correct option is A Both Assertion (A) and Reason (R) are correct and R is the correct explanation.
Using momentum conservation:
$m_{1} v = m_{1} v_{1} + m_{2} v_{2}$
Using, $e = 1$

$\Rightarrow \frac{v_{2} - v_{1}}{0 - v} = - 1$

$\Rightarrow v_{2} - v_{1} = v$
$\Rightarrow 2 m_{1} v = (m_{1} + m_{2}) v_{2}$
$\Rightarrow (m_{1} - m_{2}) v = (m_{1} + m_{2}) v_{2}$

$\Rightarrow \frac{K . E_{1}}{K . E_{2}} = \frac{\frac{1}{2} m_{1} {(\frac{m_{1} - m_{2}}{m_{1} + m_{2}})}^{2} v^{2}}{\frac{1}{2} \times \frac{m_{2} \times 4 {m_{1}}^{2}}{(m_{1} + m_{2})^{2}} v^{2}}$ $= \frac{(m_{1} - m_{2})^{2}}{4 m_{1} m_{2}}$

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Similar questions

Q. Assertion (A) : A body of "

m_{1}

" collides another body of mass "

m_{2}

" at rest elastically. The fraction of energy transferred to the second body is

\frac{m_{1}}{m_{1} + m_{2}}

Reason (R) : In an "inelastic collision" only linear momentum is conserved

Q. Assertion: Average kinetic energy in one oscillation during

SHM

of a body is

\frac{1}{4} m ω^{2} A^{2}

.
Reason: Maximum kinetic energy is

\frac{1}{2} m ω^{2} A^{2}

Assertion (A): Steel is more elastic than rubber.

Reason (R) : Under a given deforming force, steel is deformed less than rubber.

A) Both Assertion and Reason are true and the reason is correct explanation of the assertion
B)Both Assertion and Reason are true, but reason is not correct explanation of the assertion
C) Assertion is true, but the reason is false
D) Assertion is false, but the reason is true

(a) Both Assertion (A) and Reason (R) are true and Reason (A) and Reason (R). For selecting the correct answer, use the following code :

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false and Reason (R) is true.

$\begin{matrix} Assertion (A) & Reason (R) \sqrt{3} i s a n i r r a t i o n a l n u m b e r . & T h e s u m o f a r a t i o n a l n u m b e r a n d a n i r r a t i o n a l n u m b e r i s a n i r r a t i o n a l n u m b e r . \end{matrix} The correct answer is: (a)/(b)/(c)/(d).$

This question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false and Reason (R) is true.

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Assertion (A) : A body of mass "m1 " collides elastically with another body of mass "m2" at rest the ratio of the the final energy of the first body to the final energy of the second body is(m1−m2)24m1m2.Reason (R) : The collision is perfectly elastic and the coefficient of restitution is 1.

The correct option is A Both Assertion (A) and Reason (R) are correct and R is the correct explanation.Using momentum conservation:m1v=m1v1+m2v2Using, e=1⇒v2−v10−v=−1⇒v2−v1=v⇒2m1v=(m1+m2)v2⇒(m1−m2)v=(m1+m2)v2⇒K.E1K.E2=12m1(m1−m2m1+m2)2v212×m2×4m12(m1+m2)2v2 =(m1−m2)24m1m2