Question

JEE MAINS SOLVE THE ATTACHED QUESTION ❓​

Answer 1

Answer :-

The ratio of their linear momentum is 1 : 2.

Step-by-step explanation :-

Given :

Two masses of 1 g and 4 g are moving with equal kinetic energies.

To find :

Ratio of the magnitude of their linear momentum.

Solution :

∵ K.E$_1$ = K.E$_2$

$\rightarrow \bold{\frac{1}{2}m_1v_1^2}=\bold{\frac{1}{2}m_2v_2^2}$

$\rightarrow \bold{\frac{1}{2}\times1\times v_1^2}=\bold{\frac{1}{2}\times4\times v_2^2}$

$\bold{\rightarrow (\frac{V_1}{V_2})^2}=\bold{4}$

$\bold{\rightarrow \frac{V_1}{V_2}}=\bold{2}\;\; (1)$

Linear momentum (P) = mv

$\bold{\frac{P_1}{P_2}}=\bold{\frac{m_1v_1}{m_2v_2}}=\bold{\frac{1}{4}\times2}\;\;(1)$

$\bold{\frac{P_1}{P_2}}=\bold{\frac{1}{2}}$

∴ The ratio of their linear momentum is 1 : 2.