Two particles having mass M_{1} = 4 gm, M_{2} = 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

\(K_1=K_2 \) --{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