Question

Find the centre of mass of letter 'F' which is cut from a uniform metal sheet from point A.

Answer 1

Answer:

Explanation:

=> Suppose, mass / unit area of the sheet = λ

Here, metal sheet is divided in three portions 1, 2 and 3.

=> Mass of all three partions of metal sheet :

The mass of 1st portion, m₁ = 16λ

The mass of 2nd portion, m₂ = 4λ

The mass of 3rd portion, m₃ = 8λ

=> The coordinate of centre of mass of all three parts are:

For 1st portion, (x₁, y₁) = ( 1, 4 )

For 2nd portion, (x₂, y₂) = ( 3, 3 )

For 3rd portion (x₃, y₃) = ( 4, 7 ).

Position of centre of mass:

X_cm = m₁x₁ + m₂x₂ + m₃x₃ / m₁+m₂+m₃

= 16λ*1 + 4λ * 3 + 8λ * 4 / 16λ + 4λ + 8λ

= 16λ + 12λ + 32λ / 28λ

= 60λ / 28λ

= 15/7

Y_cm =  m₁y₁ + m₂y₂ + m₃y₃ / m₁+m₂+m₃

= 16λ*4 + 4λ * 3 + 8λ * 7 / 16λ + 4λ + 8λ

= 64λ + 12λ + 56λ / 28λ

= 132λ / 28λ

= 33/7