JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Work, Power & Energy

Two solids

A

and

B

of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies

(K.E)_{A} : (K.E)_{B}

will be

\frac{A}{1}

, so the value of

A

will be ______

Answer: 2

Solution

Kinetic energy and momentum are related by

K = \frac{p ^{2}}{2 m}

, so for a fixed momentum the kinetic energy varies inversely with the mass. With

p_{A} = p_{B}

\frac{K _{A}}{K _{B}} = \frac{m _{B}}{m _{A}} = \frac{2}{1}

The kinetic energies are in the ratio

2 : 1

, so the value is

2

JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Integer answer

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