Question

A body mass 3kg moving with a velocity $\left( {2\hat i + 3\hat j + 3\hat k} \right)$m/s collides with another body of mass 4kg moving with a velocity $\left( {3\hat i + 2\hat j - 3\hat k} \right)m/s$. The two bodies stick together after the collision. The two bodies stick together after the collision. The velocity of the composite body is:
$
  A.{\text{ }}\dfrac{1}{7}(4\hat i - 6\hat j - 3\hat k) \\
  B.{\text{ }}\dfrac{1}{7}(18\hat i + 17\hat j - 3\hat k) \\
  C.{\text{ }}\dfrac{1}{7}(6\hat i - 4\hat j - 6\hat k) \\
  D.{\text{ }}\dfrac{1}{7}(9\hat i - 8\hat j - 6\hat k) \\
 $

Answer 1

Hint: The term used in this question velocity means the displacement of the object in unit time. Velocity is the rate of motion, speed or action. Speed is a scalar, velocity is a vector. Velocity includes the information about direction as well as speed or we can say magnitude of velocity.

Complete step-by-step solution -
According to question;
$
  {m_1} = 3kg \\
  {m_2} = 4kg \\
  {v_1} = (2\hat i + 3\hat j + 3\hat k) \\
  {v_2} = (3\hat i + 2\hat j - 3\hat k) \\
 $ (Given)
Let us take v as the velocity of the composite body.
Therefore,
 $
  m = {m_1} + {m_2} \\
  m = 3 + 4 \\
  m = 7kg \\
 $
Now, by law of conservation of linear momentum
As we know that the total momentum before collision= total momentum after collision.
$
  {m_1}{v_1} + {m_2}{v_2} = mv \\
  3\left( {2\hat i + 3\hat j + 3\hat k} \right) + 4\left( {3\hat i + 2\hat j - 3\hat k} \right) = 7v \\
  6\hat i + 9\hat j + 9\hat k + 12\hat i + 8\hat j - 12\hat k = 7v \\
  18\hat i + 17\hat j - 3\hat k = 7v \\
  v = 1/7(18\hat i + 17\hat j - 3\hat k)m/s \\
 $

Therefore, option B is the correct answer.

The law of conservation of linear momentum was discovered by the ISSAC NEWTON.
The law of conservation of linear momentum states that if no external force acts on any object or system of objects then the total momentum of the system is always conserved. Therefore the linear momentum is as the vector quantity and can be further classified as the product of mass of an object, to its velocity. The S.I unit of linear momentum is kg m/s. There are two types of momentum: linear momentum and angular momentum. We use momentum in our daily life like for example airbags that we use in our automobiles.

Note: To take an example of momentum is how the speed of a car quickly moves down the hill. Being a vector momentum has also magnitude and direction. The term impulse and momentum both are different; impulse is not equal to momentum itself therefore it's just the increase or decrease of an object's momentum.