Question

Two bodies of mass 1 kg and 2 kg are moving with
equal kinetic energies. The ratio of their respective
speeds is
(1) 1:1
(2) √2:1
(3) 1:13
(4) 2:1​

Answer 1

Answer

Option 2) √2 : 1

$\rule{50}2$

Explanation

Given, two bodies having mass 1 kg and 2 kg. They have equal kinetic energies.

We already know that kinetic energy = ½mv²

Now, for the first body having mass = 1kg, let the velocity be $\sf v_1$

and for the body having mass = 2kg, let the velocity be $\sf v_2$

Now, for the first body, it's kinetic energy

= ½mv²

= ½ × 1 × $\sf {(v_1)}^2$

= $\sf\frac{{(v_1)}^2}{2}$

For the second body, it's kinetic energy would be

½ mv²

= 1/2 × 2 × $\sf {(v_2)}^2$

= $\sf {(v_2)}^2$

Now, both the kinetic energies are equal (given)

$\sf\implies \frac{{(v_1)}^2}{2} = {(v_2)}^2$

$\sf\implies \frac{{(v_1)}^2}{{(v_2)}^2} = 2$

(by cross multiplication)

$\sf\implies \frac{v_1}{v_2} = \frac{\sqrt{2}}{1}$

(Taking roots on both sides)

Hence, the ratio of their velocities is √2 : 1.