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Two bodies of equal masses move with uniform velocities $v$ and $3 v$ respectively. Then the ratio of their kinetic energies is__

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1 : 5

1 : 9

1 : 3

1 : 7

answer is B.

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Detailed Solution

The ratio of their kinetic energies is

1 : 9

.
Given data and assumptions:
Let the mass of each body be

m

(Since both bodies have equal mass)
Mass of first body

= m

Velocity of the first body

= v

Mass of second body

= m

Velocity of second body

= 3 v

Find the ratio of kinetic energies of the two bodies.
The formula used:
Kinetic energy,

K . E = \frac{1}{2} m v^{2}

Where,

m

is the mass of the body and

v

is the velocity of the body.
Now,
The ratio of kinetic energies of the two bodies

= \frac{Kinetic energy of the first body}{Kinetic energy of the second body}

= \frac{\frac{1}{2} m v^{2}}{\frac{1}{2} m {(3 v)}^{2}}

= \frac{1}{9}

Hence, the ratio of the kinetic energies

= 1 : 9

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