Question

two bodies of equal masses moves with uniform velocity 3v and 4 v then ratio of their k.E is respectively ​

Answer 1

Explanation:

Kinetic energy is directly proportional to the (v)^2.

Given,

v1 = 3v

v2 = 4v

Mass of two bodies are equal.

$kinetic \: energy \: \: = \: \frac{1}{2} m {v}^{2} \\ kinetic \: energy \: \alpha \: {v}^{2} \\ \frac{ke1}{ke2} \: = \: \: ( \frac{v1}{v2} ) ^{2} \\ \frac{ke1}{ke2} = \: ( \frac{3v}{4v} ) ^{2} \\ \frac{ke1}{ke2} = \: \frac{ {9v}^{2} }{ {16v}^{2} } \\ \frac{ke1}{ke2 \: } = \: \frac{9}{16}$

Here,

m is the mass of body.

v is the velocity of body.

v1 is the velocity in 1st body.

And

v2 is the velocity in 2nd body.

ke1 is the kinetic energy in 1st body.

And

ke2 is the kinetic energy in 2nd body.

Hence,

Ratio of their kinetic energy = ke1/ke2 = 9/16 = 9:16.