Question

Two bodies are with same kinetic energy and thier masses are in the ratio of 1:2 the ratio of thier velocities is?

Answer 1

Explanation:

KE 1 = KE 2 ( Kinetic energy of 1st body = Kinetic energy of 2nd body )

Let M1 = x

Then , M2 = 2x

V1 : V2 = ??

$ke \: 1 = \frac{1}{2} \times m1 \times {(v1)}^{2}$

$= \frac{x \times {(v1)}^{2} }{2}$

$ke \: 2 = \frac{1}{2} \times m2 \times {(v2)}^{2}$

$= \frac{2x \times {(v2)}^{2} }{2} = x {(v2)}^{2}$

According to the question,

KE 1 = KE 2

$\frac{x {(v1)}^{2} }{2} = x {(v2)}^{2}$

${ (\frac{v1}{v2}) }^{2} = 2$

$\frac{v1}{v2} = \frac{ \sqrt{2} }{1}$

Hence ,

V1 : V2 = square root 2 : 1

I hope it helps you. If you have any doubts, then don't hesitate to ask.