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Question

# A body of 1 kg makes an elastic collision with a second body at rest and continues to move in the original direction, but with half of its original speed. What is the mass of the second body?

A
12 kg
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B
2 kg
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C
13 kg
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D
3 kg
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Solution

## The correct option is C 13 kgGiven that m1=1 kg m2=? Let v0 be the velocity of mass m1 before collision. Now, we can apply momentum conservation because no net external force is acting on the system. m1v0+(m2×0)=m1×v02+m2v ⇒m1v0=m1v02+m2v ⇒v=m1v02m2=v02m2 ... (1) [∵m1=1 kg] From energy conservation, 12m1v20+0=12m1(v02)2+12m2v2 ⇒v202=v208+12m2v2 ⇒m2v2=34v20 Putting the value of v from eq. (1), m2(v02m2)2=34v20 ⇒m2×v204m22=34v20 ⇒v204×43v20=m2 ⇒m2=13 kg

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