Q.

The disc of mass M and radius R with uniform surface mass density  σ as shown in the figure. The centre of mass of quarter disc (the shaded area) is at the position x3Rπ,x3Rπ where   x is _____, (Round off to the Nearest integer)[a is the shaded area as shown in the figure]

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answer is 4.

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Detailed Solution

The distance of centre of mass of certain symmetrical shape of disc from centre is  d=4Rsinθ/23θ For quarter, put θ=π2      ∴d=8R32π ∴xcoordiante=dcos45=8R32π×12=4R3π    ∴ycoordiante=dsin45=8R32π×12=4R3π
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The disc of mass M and radius R with uniform surface mass density  σ as shown in the figure. The centre of mass of quarter disc (the shaded area) is at the position x3Rπ,x3Rπ where   x is _____, (Round off to the Nearest integer)[a is the shaded area as shown in the figure]