Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses $m$ , $2 m$ and $m$ , respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes a completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C. [2009]

Question

Smart Achievers · Accepted Answer

(4)

Hence, just after collision with A velocity of B

$v_{B} = \frac{(m_{B} - m_{A}) u_{B}}{m_{B} + m_{A}} + \frac{2 m_{A} u_{A}}{m_{A} + m_{B}} = \frac{0 + 2 m \times 9}{m + 2 m} = 6 m/s$

The collision between B and C is completely inelastic

$∴$ $m_{B} v_{B} = (m_{B} + m_{C}) v$

$\Rightarrow v = \frac{6 \times 2 m}{2 m + m} = 4 m/s .$

Solution

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Solution

Ans. (4) Hence, just after collision with A velocity of B vB=(mB-mA)uBmB+mA+2mAuAmA+mB=0+2m×9m+2m=6 m/s The collision between B and C is completely inelastic ∴ mBvB=(mB+mC)v ⇒ v=6×2m2m+m=4 m/s.

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