Question

(d) Two bodies have equal mass. However, the
speed of the one body is twice the speed of
other body. What is the ratio of kinetic energy
of the two bodies?​

Answer 1

Given :

Two bodies have equal mass.

the speed of the one body is twice the speed of other body.

To Find :

What is the ratio of kinetic energy of the two bodies?

Solution :

$\begin{gathered} : \implies \sf \: \: \: \: \: \: kinetic \: energy = \frac{1}{2} m {v}^{2} \\ \\ \\ : \implies \sf \: \: \: \: \: \:m1 = m2 \\ \\ \\: \implies \sf \: \: \: \: \: \: v1 = 2 \times v2 \\ \\ \\ : \implies \sf \: \: \: \: \: \:\frac{ \frac{1}{2}m {(v1)}^{2} }{ \frac{1}{2}m {(v2)}^{2} } = \frac{ {(v1)}^{2} }{ {(v2)}^{2} } \\ \\ \\ : \implies \sf \: \: \: \: \: \: = \frac{ {(2v2)}^{2} }{ {(v2)}^{2} } = \frac{4}{1} \\ \\ \\ : \implies \sf \: \: \: \: \: \: \green{4 : 1}\end{gathered}$

$\underline { \purple{4 : 1} \: is \: the \: ratio \: of \: kinetic \: energy \: of \: the \: two \: bodies}$