Question

A railway carriage of mass $10000kg$ moving with a speed $15\dfrac{m}{s}$ hits a stationary carriage of same mass. After the collision the carriage gets coupled and moves together. What is their common velocity after collision?

Answer 1

This question is based on the concept of law of conservation of momentum. This law states that for two or more bodies in an isolated system which are acting upon each other, their total momentum always remains constant until and unless an external force is applied on them. Therefore, momentum in an isolated system can neither be created nor destroyed.

Complete step by step answer:
According to the definition of the law of conservation of momentum,
${m_1}{v_1} + {m_2}{v_2} = MV......(1)$
In this question,
${m_1} = 10000kg$
${m_2} = 10000kg$
${v_1} = 15\dfrac{m}{s}$
${v_2} = 0\dfrac{m}{s}$
$M = 10000 + 10000 = 20000kg$
$V = ?$
On putting the following values in the equation (1), we get,
$10000(15) + 10000(0) = 20000(V)$
$150000 = 20000V$
On further solving, we get,
$V = \dfrac{{150000}}{{20000}}$
$V = 7.5\dfrac{m}{s}$
So, the common velocity of the system after the collision has taken place is $V = 7.5\dfrac{m}{s}$.

Note: The total momentum of any system is the vector sum of individual momenta of the different components present in the system. Hence, the component of the total momentum along any direction always remains constant. Momentum remains conserved in any of the physical processes. In this question, we have applied the concept of law of conservation of linear momentum, apart from the law of conservation of linear momentum, there is also a law of conservation of rotational momentum.