Question

10gm., 30gm and 60gm are at 20cm, 40cm
and 80cm on light metre scale. The position
of the centre of mass of the system is​

Answer 1

Given:

10gm., 30gm and 60gm are at 20cm, 40cm and 80cm on light metre scale.

To find:

Position of centre of mass ?

Calculation:

The position of a centre of mass can be calculated as follows :

$\rm \therefore \: \bar{x} = \dfrac{ \sum ( m_{i} x_{i} ) }{ \sum( m_{i}) }$

$\rm \implies \: \bar{x} = \dfrac{ (10 \times 20) + (30 \times 40) + (60 \times 80) }{ (10 + 30 + 60)}$

$\rm \implies \: \bar{x} = \dfrac{ 200 + 1200 + 4800}{ 100}$

$\rm \implies \: \bar{x} = \dfrac{ 6200}{ 100}$

$\rm \implies \: \bar{x} = 62 \: cm$

So, the centre of mass of the system is located at 62 cm mark on the scale.