Question

To spheres of masses 4 kg and 8 kg are moving
with velocities 2 ms' and 3 ms' away from
each other along the same line. Find the
velocity of centre of mass.
ms towards second sphere
1),
2); my towards second sphere
ms
away from the second sphere
WIN wtoo
ms-
away from the second sphere​

Answer 1

Given :

Two spheres of masses 4kg and 8kg are moving with velocities 2m/s and 3m/s away from each other.

To Find :

Velocity of centre of mass.

Solution :

❖ Centre of mass is an imaginary point where the whole mass of system can be assumed to be concentrated.

» Velocity of centre of mass of a two particle system is given by

$:\implies\:\underline{\boxed{\bf{\orange{v=\dfrac{m_1v_1+m_2v_2}{m_1+m_2}}}}}$

Here velocity of the sphere of 4 kg will be -2m/s as it is moving in the opposite direction with respect to the second sphere.

By substituting the given values;

$\sf:\implies\:v=\dfrac{(4)(-2)+(8)(3)}{4+8}$

$\sf:\implies\:v=\dfrac{-8+24}{12}$

$\sf:\implies\:v=\dfrac{16}{12}$

$:\implies\:\underline{\boxed{\bf{\gray{v=\dfrac{4}{3}\:ms^{-1}}}}}$

[towards the second sphere]