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 .

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 . <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-yzjxfe9cbrjdk52q.jpg" /> (A) 4 (B) 7 (C) 10 (D) 12

Tardigrade Admin · Accepted Answer

vA prime=((m-2 m/m+2 m))(9)+(2(2 m)/m+2 m)(0)=-3 m s -1 Now from conservation of linear momentum after all collisions are complete, m (+9 m s -1)= m (-3 m s -1)+3 m ( v C ) or v C =4 m s -1

$4$

$7$

$10$

$12$

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

4

7

10

12

vA′​=(m+2mm−2m​)(9)+m+2m2(2m)​(0)=−3ms−1 Now from conservation of linear momentum after all collisions are complete, m(+9ms−1)=m(−3ms−1)+3m(vC​) or vC​=4ms−1

$4$

$7$

$10$

$12$

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