NEET Class neet Answered

Figure shows the rectangular plate of length L . Left half of plate has density d₁ and right half of plate has density d₂ .

Center of mass of left half plate is at geometrical center C_L . Center of mass of right half plate is at geometrical center C_R .

Let A be the equal area of left half and right half parts of plate. Let t be the uniform thickness of plate.

Let m_L  and m_R be the masses of left side and right side plate .

Let us consider x-axis of x-y coordinate system be on the line joining the points od centre of massses  C_L and C_R .

Let Origin be the left edge of the full plate as shown in figure .

X-cooordinate X of centre of mass of full plate of length L is determined as

[ m_L+ m_R ] X  = m_L × (L/4) + m_R × (3L/4)  ......................... (1)

mass of plates are

m_L = A × t × d₁ ............................(2)

m_R = A × t × d₂ .........................(3)

By substituting the masses from eqn.(2) and eqn.(3) , we rewrite eqn.(1) after simplification as

[ d₁ + d₂ ] X   =  (L/4) ( d₁ + 3 d₂ )

X-cooordinate X of centre of mass of full plate of length L is