Question

two bodies have equal mass. the speed of one body is thrice the speed of other body. find the ratio of their kinetic energy ​

Answer 1

Answer: Two bodies have equal mass. The speed of one body is thrice the speed of other body. The ratio of their kinetic energy is 9 : 1 ​if the speed of the first body is three that of the second body.

Explanation

Let A  be the first body and B  be the second body, the equation for Kinetic Energy of a body

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

where $m$  is the mass of the body and $v$ is the velocity or speed of the body.

As the mass of the first body is equal to the mass of other body and speed is thrice of the second body,

Kinetic energy of the first body can be substituted as,

$E= \frac{1}{2} m(3v)^{2}$

and  

Kinetic energy of the second body can be substituted as,

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

Therefore the ratio of the two bodies is

$\frac{E(A)}{E(B)} =\frac{\frac{1}{2}m(3v)^{2} }{\frac{1}{2}mv^{2} } =\frac{9}{1}$

Therefore the ratio of their kinetic energy is 9 : 1