Question

Two bodies A and B moving with the same velocity have their masses in the ratio of 1 : 4. What will be the ratio of their kinetic energy?

Answer 1

Let the masses be m and 4m (As given in the ratio)

Now formula of kinetic energy =1/2mv^2

So putting m and 4m in the kinetic energy formula.

K1=1/2mv^2

K2=1/2×4mv^2

K1=1/mv^2/K2=4 (1/2mv^2)

So the ratio is 1:4

I hope the answer is right if it is not i am sorry

Answer 2

The ratio of the Kinetic energy will be 1:4

Suppose, the mass of object A is = m₁

And, the mass of the object B is = m₂

Give,

The two bodies have same velocity (v)

Now, according to the formula of Kinetic Energy,

K.E. = $\frac{1}{2}mv^2$

As the velocity is same of the two objects,

K.E. ∝ m

Give,

The ratio of masses of A  and B are,

m₁ : m₂ = 1 : 4

So, the ratio of the kinetic energies will be 1:4