A stationary particle explodes into two parti | vedclass

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(D) According to the law of conservation of linear momentum,since the initial particle is stationary,the total initial momentum is $0$.$0 = x v_1 - y

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$\frac{y}{x}$

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(D) According to the law of conservation of linear momentum,since the initial particle is stationary,the total initial momentum is $0$.$0 = x v_1 - y v_2$ (taking opposite directions as positive and negative)$x v_1 = y v_2 \implies \frac{v_1}{v_2} = \frac{y}{x} \dots (1)$The kinetic energy of a particle is given by $E = \frac{1}{2} m v^2$.The ratio of kinetic energies is:$\frac{E_1}{E_2} = \frac{\frac{1}{2} x v_1^2}{\frac{1}{2} y v_2^2} = \frac{x}{y} \left( \frac{v_1}{v_2} \right)^2$Substituting equation $(1)$ into the expression:$\frac{E_1}{E_2} = \frac{x}{y} \left( \frac{y}{x} \right)^2 = \frac{x}{y} \cdot \frac{y^2}{x^2} = \frac{y}{x}$Thus,the ratio is $\frac{y}{x}$.

$A$ stationary particle explodes into two particles of masses $x$ and $y$,which move in opposite directions with velocities $v_1$ and $v_2$. The ratio of their kinetic energies $(E_1: E_2)$ is

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