Question

Two masses are in the ratio 1:4 have their speeds in the ratio 4:5 find the ratio of their kinetic energy

Answer 1

Ratio of masses = M1:M2 = 1:4

Ratio of Speeds = V1:V2 = 4:5

$kinetic \: energy = \frac{1}{2} m {v}^{2}$

$ratio \: = \: \frac{ \frac{1}{2}m1 \times {v1}^{2} }{ \frac{1}{2}m2 \times {v2}^{2} } = \frac{1 \times 4 \times 4}{4 \times 5 \times 5} = \frac{4}{25}$

Required Ratio = 4:25