Question

Two particles having mass M₁ = 4 gm, M₂ = 16 gm. If kinetic energy of both the particle is equal then ratio of their momentum is n : 2 then n is:

(1) 2 

(2) 1/2 

(3) 4 

(4) 1/4

Answer 1

\(K_1=K_2 \) --{given}
⇒\(\tfrac{p_1^2}{2m_1}=\tfrac{p_2^2}{2m_2}\) 
⇒\((\tfrac{p_1}{p_2})^2=\tfrac{m_1}{m_2}\)
⇒\((\tfrac{p_1}{p_2})=\sqrt{\tfrac{m_1}{m_2}}\) 
⇒\(\sqrt{m_1}:\sqrt{m_2}\)
given m1=4g m2=16g
⇒\(\sqrt{4}:\sqrt{16}\)
⇒\(\sqrt{1}:\sqrt{4}\) ⇒1:2n:2 = 1:2
therefore n=1

The answer is option 2) 1/2 , and value of n=1