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

Answer:-

Let mass of first body = mass of second body = m.

Given:

Speed / velocity of first body is twice the second body.

Let velocity of second body = v

So, velocity of first body = 2v

We know that,

Kinetic energy (KE) = 1/2 mv².

So,

Required ratio of their KEs is :

1/2 m(2v)² : 1/2 mv²

⟶ 4v² : v²

⟶ 4 : 1

∴ The ratio of their kinetic energies is 4 : 1 or 1 : 4.

Answer 2

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 :

$: \implies \sf \: \: \: \: \: \: kinetic \: energy = \frac{1}{2} m {v}^{2} \\ \\ \\ : \implies \sf \: \: \: \: \: \:m1 = m2 \\ \\ \\: \implies \sf \: \: \: \: \: \: v1 = 2 \times v2 \\ \\ \\ : \implies \sf \: \: \: \: \: \:\frac{ \frac{1}{2}m {(v1)}^{2} }{ \frac{1}{2}m {(v2)}^{2} } = \frac{ {(v1)}^{2} }{ {(v2)}^{2} } \\ \\ \\ : \implies \sf \: \: \: \: \: \: = \frac{ {(2v2)}^{2} }{ {(v2)}^{2} } = \frac{4}{1} \\ \\ \\ : \implies \sf \: \: \: \: \: \: \red{4 : 1}</p><p>$

$\underline \mathfrak{ \pink{4 : 1} \: is \: the \: ratio \: of \: kinetic \: energy \: of \: the \: two \: bodies}</p><p>$