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NEET 2003

Exam: NEET
Year: 2003
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

NEET 2003 · Physics · Center of Mass, Momentum and Collision

A stationary particle explodes into two particles of masses m_1 and...

A stationary particle explodes into two particles of masses

m_1

and

m_2

which more in opposite direction with velocities

v_1

and

v_2

. The ratio of their kinetic energies

E_1 / E_2

is:

Options

A $m_2 / m_1$
B $m_1 / m_2$
C1
D $m_1 m_2 / m_2 m_1$

Correct answer

A. $m_2 / m_1$

Step-by-step solution

According to law of conservation of linear momentum

\begin{aligned}& m_1 v_1=m_2 v_2 \quad \ldots \text{ (i) }\\ & E_1=\frac{1}{2}m_1 v_1^2, E_2=\frac{1}{2}m_2 v_2^2 \\ & \therefore \frac{E_1}{E_2}=\frac{\frac{1}{2} m_1 v_1^2}{\frac{1}{2} m_2 v_1^2}=\frac{\left(m_1 v_1\right)^2}{\left(m_2 v_2\right)^2} \times \frac{m_2}{m_1}\\ & \therefore \frac{E_1}{E_2}=\frac{m_2}{m_1} \end{aligned}

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