The centre of mass of a body is a point at which the entire mass of the body is supposed to be concentrated. The position vector `overset rarr(r )` of c.m of the system of tow particles of masses `m_(1)` and `m_(2)` with position vectors `overset rarr(r_(1))` and `overset rarr(r_(2))` is given by
`overset rarr(r ) = (m_(1)overset rarr(r_(1)) + m_(2)overset rarr(r_(2)))/(m_(1) + m_(2))`
For an isolated system, where no external force is acting, `overset rarr(v_(cm)) =` constant
Under no circumstances, the velocity of centre of mass of an isolated system can undergo a change
With the help of the comprehension given above, choose the most appropriate alternative for each of the following questions :
Two bocls of masses `5 kg` and `2 kg` are placed on a frictionless surface and connected by a spring. an external kick gives a velocity of `14 m//s` to heavier block in the direction of lengter one. the velocity gained by the centre of mass is

Options

A. `14 m//s`
B. `7 m//s`
C. `12 m//s`
D. `10 m//s`

Answer

D

Explanation

Here, `m_(1) = 5kg, m_(2) = 2kg`
`v_(1) = 14 m//s v_(2) = 0, v_(cm) = ?`
`v_(cm) = (m_(1)v_(1) + m_(2)v_(2))/(m_(1) + m_(2)) = (5 xx 14 + 2 xx 0)/(5 + 2) = (70)/(7)`
`= 10 m//s`