Two particles having masses 4, g and 16, g re | vedclass

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(A) The kinetic energy $K$ of a particle with mass $m$ and linear momentum $p$ is given by the formula $K = \frac{p^2}{2m}$.Since the kinetic energies

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(A) The kinetic energy $K$ of a particle with mass $m$ and linear momentum $p$ is given by the formula $K = \frac{p^2}{2m}$.Since the kinetic energies of the two particles are equal,we have $K_1 = K_2$.Substituting the formula,we get $\frac{p_1^2}{2m_1} = \frac{p_2^2}{2m_2}$.Given $m_1 = 4\, g$ and $m_2 = 16\, g$,we have $\frac{p_1^2}{2 	imes 4} = \frac{p_2^2}{2 	imes 16}$.Simplifying this,$\frac{p_1^2}{4} = \frac{p_2^2}{16}$,which implies $\frac{p_1^2}{p_2^2} = \frac{4}{16} = \frac{1}{4}$.Taking the square root of both sides,$\frac{p_1}{p_2} = \frac{1}{2}$.We are given that the ratio of the magnitudes of their linear momentum is $n : 2$,so $\frac{p_1}{p_2} = \frac{n}{2}$.Comparing $\frac{n}{2} = \frac{1}{2}$,we find $n = 1$.

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

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