Question

Two particles of mass 10 g and 40 g are moving with same kinetic energy, then ratio of linear momentum is:
1. 4 : 1
2. 1 : 4
3. √2 : 1 
4. 1 : 2

Answer 1

Correct Answer - Option 4 : 1 : 2

CONCEPT :

• The kinetic energy of a particle is the energy acquired by the particle due to the motion of the particle.
  • The linear momentum of an object is the product mass and velocity of  the particle 
• The relationship between the momentum and kinetic energy is given by

\(\Rightarrow K = \frac{P^{2}}{2 m}\)

Where K = kinetic energy , P = momentum , m =  mass 

• The ratio of two momentum P₁ and  P₂ is given by

\(\Rightarrow \frac{P_{1}}{P_{2}} = \sqrt{\frac{m_{1}}{m_{2}}}\)

CALCULATION :

Given m₁ = 1 , m₂ = 4 

• The ratio of two momentum P1 and  P2 is given by

\(\Rightarrow \frac{P_{1}}{P_{2}} = \sqrt{\frac{m_{1}}{m_{2}}}\)

\(\Rightarrow \frac{P_{1}}{P_{2}} = \sqrt{\frac{1}{4}} = \frac{1}{2}\)

• Hence, option 4 is the answer