Question

Two bodies of mass 1 kg and 2 kg are moving with equal kinetic energies. The ratio of their respective speeds is

Answer 1

$\large{\implies{Answer}}$

For first object :

$k = \frac{1}{2} mv {}^{2} \\ k = \frac{1}{2} (1kg)v {}^{2} \\ 2k = v {}^{2}$

For second object :

$k = \frac{1}{2} mv {}^{2} \\ k = \frac{1}{2} (2kg)v {}^{2} \\ k = v {}^{2}$

✏ Ratio of thier velocities :

$\frac{v {}^{2} }{v {}^{2} } = \frac{k {}^{} }{2k {}^{} }$

✏ 1:2

Answer 2

Answer:

Given values

mass of 1st body ( m1 ) = 1kg

mass of 2nd body (m2 ) = 2kg

Kinetic energy of two bodies

Energy of 1st body :-

K.E = 1/2 . mv²

K.E = 1/2 . (1) . v²

K.E = 1/2 . v²

v² = 2k ====> eqn 1

Energy of 2nd body :-

K.E = 1/2.mv²

K.E = 1/2 . (2) . v²

K.E = 2/2 .v²

K.E = 1.v²

v² = 1k ===> eqn 2

From eqn 1 and 2

[ Divide eqn 1 and 2 on both sides ]

===> eqn 1 / eqn 2

===> v² / v² = k / 2k

===> 1 = 2k

Ratio of their respective speeds

1 : 2