Question

Q1. Two bodies of equal masses move with uniform velocities v and 3 v
respectively. Find the ratio of their kinetic energies. [5 marks]
Your answer​

Answer 1

Answer:

$\boxed{\mathfrak{Ratio \ of \ Kinetic \ Energies = 1:9}}$

Given:

Two bodies of equal mass = m

Velocity of first body $\sf v_1$ = v

Velocity of second body $\sf v_2$ = 3v

To Find:

Ratio of Kinetic Energies.

Explanation:

Kinetic Energy:

$\boxed{ \bold{KE = \dfrac{1}{2} m {v}^{2} }}$

As mass of body bodies are same. So,

$\bold{ KE \propto {v}^{2} }$

$\therefore \\ \sf Kinetic \: Energy \: of \: first \: o body: \\ \sf KE_1 \propto v^2 \\ \\ \sf Kinetic \: Energy \: of \: second \: o body: \\ \sf KE_2 \propto (3v)^2$

Ratio of Kinetic Energy:

$\sf \implies \dfrac{KE_1}{KE_2} = \dfrac{ {v}^{2} }{ {(3v)}^{2} } \\ \\ \sf \implies \dfrac{KE_1}{KE_2} = \dfrac{ \cancel{ {v}^{2}} }{9 \cancel{ {v}^{2}} } \\ \\ \sf \implies \dfrac{KE_1}{KE_2} = \dfrac{1 }{9 } \\ \\ \sf \implies KE_1:KE_2 = 1:9$

Answer 2

Answer:

$\frac{KE_1}{KE_2} = \frac{ \frac{1}{2}m {v}^{2} }{ \frac{1}{2} m {(3v)}^{2} } \\ \\ \frac{KE_1}{KE_2} = \frac{1}{9} \\ \\ KE_1:KE_2 =1:9$