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Locate ,the centre of mass of the unifor...

Locate ,the centre of mass of the uniform then L-shaped body as shown in Fig. Assume its thickness to be t and density `rho`.

Text Solution

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The correct Answer is:
`x cm = 1.35 m, y cm = -0.23 m`
With respect to origin the C.M. of the rectangle A is `x_(A)=1.0 m`
`y_(A) = 0.10` m and that of the rectangle B is `x_(B) = (1.80 + 0.10) = 1.90 m`,
`y_(B)=-0.74 m, m_(A) =2 xx 0.2 xx trho = 0.4 rho tm^(2), m_(B) = 1.48 xx 0.2 xx rhot = -0.26 rho tm^(2)`
`x_( cm) = m_(A)x_(A) + m_(B)x_(B)//m_(A) + m_(B) = 0.4 rho t xx 1 + 0.26 rho xx 1.9//0.4 rhot + 0.26 rhot = 1.35 m`
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