Question

Match the following, if a body has intial and final kinetic energies as $K.E_1$ and $K.E_2$ respectively.

• A. $v_2=\sqrt{2}{v}_1$
• B. $v_2=3v_1$
• C. $v_2=4v_1$

Answer 1

Kinetic energy $=\frac{1}{2}m{v}^2$, where $m$ is the mass of the object, $v$ is the velocity of the object.
Given,
Intial kinetic energy $K.E_1$ = $\frac{1}{2}m{v}_1^2$.
Case - I
When $v_2$ = $\sqrt{2}{v}_1$
$K.E_2$ = $\frac{1}{2}m{v}_2^2$
= $\frac{1}{2}m(\sqrt{2}{v}_1{)}^2$
$K.E_2$ = $2K.E_1$
Case-II
When $v_2=3v_1$, $K.E_2$ = $9K.E_1$
Case-III
When $v_2=4v_1$, $K.E_2$ = $16K.E_1$