Three objects A, B and C are kept in a straight line on a frictionless surface. These have masses m, 2 m and 2 m, respectively. The object A moves towards B with a speed 9 m / s and makes an elastic collision with it. Thereafter, B makes an elastic collision with C. All motions occur on the same straight line. The final speed (in m / s ) of object B is found to be x. Find the value of ' x '.

Question

Three objects A, B and C are kept in a straight line on a frictionless surface. These have masses m, 2 m and 2 m, respectively. The object A moves towards B with a speed 9 m / s and makes an elastic collision with it. Thereafter, B makes an elastic collision with C. All motions occur on the same straight line. The final speed (in m / s ) of object B is found to be x. Find the value of ' x '. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Collision between A and B, m × 9=m1+2 m v2 9=v1+2 v2 ...(1) e=1=((v2-v1)/9) v2-v1=9 ...(2) from (1) and (2) v2=6 m / s

2 m × 6=3 m × v 3 v 3=4 m / s

Collision between A and B, m×9=m1​+2mv2​ 9=v1​+2v2​...(1) e=1=9(v2​−v1​)​ v2​−v1​=9...(2) from (1) and (2) v2​=6m/s 2m×6=3m×v3​ v3​=4m/s

Collision between $A$ and $B$ ,
$m \times 9 = m_{1} + 2 m v_{2}$
$9 = v_{1} + 2 v_{2} ... (1)$
$e = 1 = \frac{( v _{2} - v _{1} )}{9}$
$v_{2} - v_{1} = 9 ... (2)$
from (1) and (2)
$v_{2} = 6 m / s$

$2 m \times 6 = 3 m \times v_{3}$
$v_{3} = 4 m / s$