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Question
A car is running at a speed of 15 km h-1 while another similar car is moving at a speed of 45 km h-1. Find the ratio of their kinetic energies.
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Solution
Given, velocity of first car, v1 = 15 km/h
And velocity of second car, v2 = 45 km/h
Since masses are same, kinetic energy is directly proportional to the square of the velocity (Kav2)
Hence, ratio of their kinetic energies is:
`therefore k_1/k_2 = v_1^2/v_2^2`
`therefore k_1/k_2 =15^2/45^2`
`therefore k_1/k_2 = (cancel(15)^1 xx cancel(15)^1)/(cancel(45)_3 xx cancel(45)_3)`
`therefore k_1/k_2 = 1/(3 xx 3)`
`therefore k_1/k_2 = 1/9`
∴ k1 / k2 = 1 : 9
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