A wireframe is made of a wire of uniform cross-section which is shown in figure. ABC, HGF and DIE are semicircular arcs of radius r. CD = DO = OE = EF = r and 'O' is the centre of circle. Then centre of mass of frame is :

Engineering

Physics

Center of Mass

Calculus

Forces and Types of Forces

Question

A wireframe is made of a wire of uniform cross-section which is shown in figure. ABC, HGF and DIE are semicircular arcs of radius r. CD = DO = OE = EF = r and 'O' is the centre of circle. Then centre of mass of frame is :

At distance $(\frac{2 r}{3 π + 4})$ towards right of O

At distance $(\frac{4 r}{3 π + 4})$ towards left of O

At distance $(\frac{3 r}{3 π + 4})$ towards right of O

At distance $(\frac{2 r}{3 π + 4})$ towards left of O.

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$X_{C} = \frac{λ \times πR \times R + O - λ \times πR \times \frac{2 R}{π} - λ \times πR \times R}{λ (3 πr + 4 r)} = \frac{- 2 R}{3 π + 4}$ .