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}
⇒$\frac{p_1^2}{2m_1}=\frac{p_2^2}{2m_2}$ 
⇒$(\frac{p_1}{p_2}{)}^2=\frac{m_1}{m_2}$
⇒$(\frac{p_1}{p_2})=\sqrt{\frac{m_1}{m_2}}$ 
⇒$\sqrt{m_1}:\sqrt{m_2}$
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