Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of magnitudes of their linear momentum is n ∶ 2. The value of n will be ______. 

CONCEPT:

The kinetic energy is defined as the ratio of the square momentum and twice the mass and it is written as;

K.E. = \(\frac{p^2}{2m}\)

here we have p as the momentum and m as the particle's mass.

CALCULATION:

The mass of particle 1 = 4 g

and mass of the particle 2 = 16 g

The kinetic energy of particle 1  = \(\frac{p_1^2}{2\times 4}\) = \(\frac{p_1^2}{8}\)

and kinetic energy of the particle 2 = \(\frac{p_2^2}{2\times 16}\) = \(\frac{p_2^2}{32}\)

The kinetic energy of particle 1 equals the kinetic energy of particle 2.

\(\frac{p_1^2}{8}\) = \(\frac{p_2^2}{32}\)

⇒ \(\frac{p_1^2}{p_2^2}\) = \(\frac{1}{4}\)

⇒ \(\frac{p_1}{p_2}\) = \(\frac{1}{2}\)

Therefore, n = 1

Hence, n = 1.