Question

Two bodies of masses 4 kg and 5 kg are moving with equal momentum. The ratio of their respective Kinetic Energy will be
1. \(\sqrt 4 \;:\sqrt 5\)
2. 16 : 25
3. 25 : 16
4. 5 : 4

Answer 1

Correct Answer - Option 4 : 5 : 4

CONCEPT:

• Momentum: Momentum of the body is equivalent to the product of mass and velocity.

P = m v, where P is momentum, m is mass of the body; v is the velocity of the body.

• Kinetic energy: It is the energy of the body associates with its motion.

K = ½ m v², where K is kinetic energy, m is mass; v is the velocity of the body.

CALCULATION:

Given that mass m₁ = 4 kg, m₂ = 5 kg and P₁ = P_2.

\(\frac{{{{\rm{P}}_1}}}{{{{\rm{P}}_2}}} = \frac{{{{\rm{m}}_1}{{\rm{v}}_1}}}{{{{\rm{m}}_2}{{\rm{v}}_2}}}\) 

\(\frac{{{{\rm{P}}_1}}}{{{{\rm{P}}_2}}} = \frac{{4{{\rm{v}}_1}}}{{5{{\rm{v}}_2}}}\)_, hence, P₁ = P₂

\(\frac{{{{\rm{v}}_1}}}{{{{\rm{v}}_2}}} = \frac{5}{4}\) 

From the kinetic energy equation,

\(\frac{{{{\rm{k}}_1}}}{{{{\rm{k}}_2}}} = \frac{{\frac{1}{2}{{\rm{m}}_1}{\rm{v}}_1^2}}{{\frac{1}{2}{{\rm{m}}_1}{\rm{v}}_2^2}}\) 

\(\frac{{{k_1}}}{{{k_2}}} = \frac{4}{{5}} \times {\left[ {\frac{5}{4}} \right]^2}\) 

\(\frac{{{k_1}}}{{{k_2}}} = \frac{5}{{4}}\),

So, the answer will be 5 : 4.