Q.

Half of the rectangular plate shown in figure is made of a material of density ρ1 and the other half of density ρ2. The length of the plate is L. The centre of mass of the system from O is

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a

L2

b

(ρ1+3ρ2)4(ρ1+ρ2)L

c

(3ρ1+ρ2)(ρ1+ρ2)L

d

Mx = m(L cos θ-x)

answer is B.

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Detailed Solution

Let area of each half is A and thickness of the plate is t.mass of Ieft half = m1 = ρ1 At, x1= L4mass of right half = m2 = ρ2 At, x2 = 3L4Now apply xcm = m1x1+m2x2m1+m2 = ρ1L+3ρ2L4(ρ1+ρ2)
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