A moving particle of mass m, makes a head on elastic collision with another particle of mass 2m, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to ..........

Question

A moving particle of mass $m$ , makes a head on elastic collision with another particle of mass $2 m$ , which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to ..........

Smart Achievers · Accepted Answer

(89)

Fractional decrease in kinetic energy of mass $2 m$

$= 1 - {(\frac{m_{2} - m_{1}}{m_{2} + m_{1}})}^{2} = 1 - {(\frac{2 - 1}{2 + 1})}^{2} = 1 - {(\frac{1}{3})}^{2} = 1 - \frac{1}{9} = \frac{8}{9}$

Percentage loss in energy $= \frac{8}{9} \times 100 \approx 89 %$

Solution

Q.
A moving particle of mass $m$ , makes a head on elastic collision with another particle of mass $2 m$ , which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to ..........

Ans.
(89)

Fractional decrease in kinetic energy of mass $' m'$

$= 1 - {(\frac{m_{2} - m_{1}}{m_{2} + m_{1}})}^{2} = 1 - {(\frac{2 - 1}{2 + 1})}^{2} = 1 - {(\frac{1}{3})}^{2} = 1 - \frac{1}{9} = \frac{8}{9}$

Percentage loss in energy $= \frac{8}{9} \times 100 \approx 89 %$

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Solution

Q. A moving particle of mass m, makes a head on elastic collision with another particle of mass 2m, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to ..........

Ans. (89) Fractional decrease in kinetic energy of mass 'm' =1-(m2-m1m2+m1)2=1-(2-12+1)2=1-(13)2=1-19=89 Percentage loss in energy =89×100≈89%

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Q.
A moving particle of mass $m$ , makes a head on elastic collision with another particle of mass $2 m$ , which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to ..........

Ans.
(89)

Fractional decrease in kinetic energy of mass $' m'$

$= 1 - {(\frac{m_{2} - m_{1}}{m_{2} + m_{1}})}^{2} = 1 - {(\frac{2 - 1}{2 + 1})}^{2} = 1 - {(\frac{1}{3})}^{2} = 1 - \frac{1}{9} = \frac{8}{9}$

Percentage loss in energy $= \frac{8}{9} \times 100 \approx 89 %$