Question

A system consisting of two objects has a total momentum of (18 kgm/s)\(\hat{I}\)and its centre of mass has the velocity of (3 m/s)\(\hat{I}\). One of the object has the mass 4 kg and velocity (1.5 m/s)\(\hat{I}\). The mass and velocity of the other objects are

Answer 1

Given,

Total momentum = (18 kgm/s)\(\hat{I},\)

Velocity of centre of mass = (3 m/s)\(\hat{I},\)

Mass of one object = 4 kg,

Velocity of the objet = (1.5 m/s)\(\hat{I},\)

Let m be the mass of other object and be the velocity.

Now we know total momentum = Total mass × velocity of centre of mass

(18 kgm/s)\(\hat{I},\)= ( + 4)(3 m/s)\(\hat{I},\)

or m = 2 kg

Now, v_cm = \(\frac{m_1v_1+m_2v_2}{m_1+m_2}\)

Or, 3i = (4×1.5i + 2v)/6

So, 18i = 6i + 2v

Or, v = 6i m/s.