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प्रश्न
Solve the following problem.
A lighter object A and a heavier object B are initially at rest. Both are imparted with the same linear momentum. Which will start with greater kinetic energy: A or B or both will start with the same energy?
उत्तर
- Let m1 and m2 be the masses of light object A and heavy objects B and v1 and v2 be their respective velocities.
- Since both are imparted with the same linear momentum,
m1v1 = m2v2 - The kinetic energy of the lighter object A
= K.E.A = `1/2 "m"_1"v"_1^2`
The kinetic energy of the heavier object B
= K.E.B = `1/2 "m"_2"v"_2^2`
∴ `("K.E."_"A")/("K.E."_"B") = (1/2 "m"_1"v"_1^2)/(1/2"m"_2"v"_2^2) = (("m"_1"v"_1)^2//"m"_1)/(("m"_2"v"_2)^2//"m"_2)`
∴ `("K.E."_"A")/("K.E."_"B") = "m"_2/"m"_1` ....[∵ m1v1 = m2v2] - As m1 < m2, therefore K.E.A > K.E.B i.e, the lighter body A has more kinetic energy.
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