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A particle moving with kinetic energy of 3 J makes a head - on collision with a stationary particle which has twice the mass. During the impact.
a) The minimum kinetic energy of the system is 1 J

b) The maximum elastic potential energy of the system is 2 J

c) Momentum and total energy are conserved at every instant.

d) The ratio of kinetic energy to potential energy of the system first decreases and then increases.

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only a, b are true

only a, b, c are true

a, b, c, d are false

a, b, c, d are true.

answer is A.

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Detailed Solution

T.E = 3 J

Max loss in K.E $= \frac{1}{2} \frac{m_{1} m_{2}}{m_{1} + m_{2}} {(u_{1} - u_{2})}^{2}$

$= \frac{1}{2} \times \frac{m \times 2 m}{3 m} u^{2}$

$= \frac{2}{3} (\frac{1}{2} {mu}^{2})$

$= \frac{2}{3} (3)$

$= 2 J$

Mm K.E of the system = 1 J

Max elastic P.E $= 3 - 1 = 2J$

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