Question

Two identical spheres of mass ' m' are placed at the two vertices of an equilateral triangle. A sphere of mass ' 2 m' is placed at the third vertex. The centre of mass of the whole system will be at [Each side of the triangle is 8 cm]

विकल्प

• `2sqrt(3), 4sqrt(3)`

• `2sqrt(3), 2`

• `4, 2sqrt(3)`

• `4, 4sqrt(3)`

Answer 1

`4, 2sqrt(3)`

Explanation:

In ΔADB,

AD = `sqrt(3)/2 xx AB = sqrt(3)/2 xx 8`

∴ AD = `4sqrt(3)` cm

The location of the centre of mass

`bar(x) = (m_1x_1 + m_2x_2 + m_3x_3)/(m_1 + m_2 + m_3)`

= `(m xx 0 + m xx 8 + 2m xx 4)/(m + m + 2m) = (16  m)/(4  m)` = 4

`bary = (m_1y_1 + m_2y_2 + m_3y_3)/(m_1 + m_2 + m_3)`

= `(m xx 0 + m xx 0 + 2m xx AD)/(m + m + 2m)`

= `(2m xx 4sqrt(3))/(4m)`

= `2sqrt(3)`