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Standard XII

Physics

Distance

In a pool gam...

Question

In a pool game, a 1 kg pool ball moving at +10 m/s strikes a 2 kg pool ball that is initially at rest. Identify which statements is true immediately after the elastic collision?

The 1 kg pool ball be at rest

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The 2 kg ball must have a negative velocity.

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The 2 kg ball's speed must be less than 10 m/s.

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The two pool balls stick together.

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The total kinetic energy of the two pool balls must be equal to 100 J

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Solution

The correct option is D The 2 kg ball's speed must be less than 10 m/s.
Given : $m_{1} = 1 k g$ $m_{2} = 2 k g$ $u_{1} = 10 m / s$ $u_{2} = 0$ $e = 1$
Using $V_{2} = \frac{(m_{2} - e m_{1}) u_{2} + (1 + e) m_{1} u_{1}}{m_{1} + m_{2}}$

$∴$ $V_{2} = \frac{(2 - 1 \times 1) \times 0 + (1 + 1) 1 \times 10}{1 + 2} = \frac{20}{3} m / s$
Hence option C is correct.

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In a pool game, a 1 kg pool ball moving at +10 m/s strikes a 2 kg pool ball that is initially at rest. Identify which statements is true immediately after the elastic collision?

The correct option is D The 2 kg ball's speed must be less than 10 m/s.Given : m1=1kg m2=2kg u1=10m/s u2=0 e=1Using V2=(m2−em1)u2+(1+e)m1u1m1+m2∴ V2=(2−1×1)×0+(1+1)1×101+2=203m/sHence option C is correct.