Question

A light and heavy body have equal momentum. Which one has greater kinetic energy?

• A. Light body
• B. Heavy body
• C. Both body have same kinetic energy
• D. None of the above

Answer 1

The correct option is

A

Light body

Assume the weight of light body is m₁ and the weight of heavy body is m₂ and momentum is p₁ and p₂ respectively. Since momentum is equal then p₁ = p₂

We know, Kinetic energy = $\frac{P^2}{2m}$

Kinetic energy of light body = $\frac{{P_1}^2}{{2m}_1}$

Kinetic energy of heavy body = $\frac{{P_2}^2}{{2m}_2}$

Given p₁ = p₂

Ratio of kinetic energy of light and heavy body = $\frac{\frac{{P_1}^2}{{2m}_1}}{\frac{{P_1}^2}{{2m}_1}}$ = $\frac{m_2}{m_1}$

Given ( m2 > m1 )

$\frac{K{E}_1}{K{E}_2}=\frac{m_2}{m_1}$

$K{E}_2<K{E}_1$

So, the kinetic energy of lighter body is higher than the kinetic energy of heavier body.