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Question
Two bodies having equal masses are moving with uniform speeds of v and 2v respectively. Find the ratio of their kinetic energies.
Solution
Let the masses of the two bodies be (m1) = m kg and (m2) = m kg .
Velocity of the first body, (v1) = v m/s
Velocity of the first body, (v2) = 2v m/s
The required ratio is-
= `"(Kinetic energy)"_1/"(Kinetic energy)"_2`
= `(1/2 (m_1)(v_1)^2)/(1/2 (m_2)(v_2)^2)`
So put the values to get ,
= `(1)^2/(2)^2`
= `1/4`
The ratio of K.E is, K.E of body 1 : K.E of body 2 = 1 : 4.
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