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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Solution

Step 1: Given
The mass of the two particles is $4 g (m_{1})$ and $16 g (m_{2})$
The kinetic energy of the particles is equal.
The ratio of the magnitudes of their linear momentum is $n : 2 (P_{1} : P_{2})$ .
Step 2: Solution
Let the momentum of the particles be $P_{1}$ and $P_{2}$
From the relation between the kinetic energy and momentum
$K E = \frac{P^{2}}{2 m}$
$\Rightarrow P = \sqrt{2 m (K E)}$
The ratio of the momentum of the particles is
$\Rightarrow \frac{P_{1}}{P_{2}} = \frac{\sqrt{2 (4 g) (K E)}}{\sqrt{2 (16 g) (K E)}} \Rightarrow \frac{n}{2} = \sqrt{\frac{1}{4}} [F r o m G i v e n] \Rightarrow n = 1$
Hence, the value of $n$ will be $1$ .

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

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_____.