Question

Two objects A and B of mass m and 4 m have the same kinetic energy. What is the ratio of the magnitude of velocities of A and B?

Answer 1

Given,

Mass of A = m

Mass of B = 4m

Kinetic energy of A = Kinetic energy of B

We know,

Kinetic energy = `1/2 "mv"^2`

So,

`1/2` × m × v_A² = `1/2` × 4m × v_B²

v_A² = 4v_B²

`(v_A^2)/(v_B^2) = 4`

`(v_A)/(v_B) = 2`

Hence, the ratio of the magnitude of velocities of A and B is 2 : 1.