Question

Three objects $A$ , $B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m$ , $2m$ and $m$ , respectively. The object $A$ moves towards $B$ with a speed $9 \, m \, s^{- 1}$ and makes an elastic collision with it. Thereafter, $B$ makes completely inelastic collision with $C$ . All motions occur on the same straight line. Find the final speed (in $m \, s^{- 1}$ ) of the object $C$ .

• A. $4$
• B. $7$
• C. $10$
• D. $12$

Answer 1

Answer: (A)

$v_{A}^{\prime}=\left(\frac{m-2 m}{m+2 m}\right)(9)+\frac{2(2 m)}{m+2 m}(0)=-3 m s ^{-1}$
Now from conservation of linear momentum after all collisions are complete,
$m \left(+9 m s ^{-1}\right)= m \left(-3 m s ^{-1}\right)+3 m \left( v _{ C }\right)$
or $\quad v _{ C }=4 m s ^{-1}$