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A thin uniform rod oflength "L" is bentits mid point as shown in the figure.distance of the centre of mass from the p"O" is

A thin uniform rod oflength "L" is bentits mid point as shown in the figure.distance of the centre of mass from the p"O" is

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Grade:11

1 Answers

Vedanshi
16 Points
6 years ago
Length of rod =LNow as it bends from its mid point ,Length of each segment is =L/2As it is a uniform rod ,Therefore considering 1st n 2nd segment of rod separately COM of each segment =L/4Now since 1st segment is along d X axis & 2nd makes an angle `@` with -ve X axis ..... Or `180-@` with +ve X axis By applying Xcm={ (m/2)×(-l/4) + (l/4cos(180-@))}÷(m/2+m/2)=. -l(1+cos)/8Similarly for Ycm ={ (m/2)×l/4sin(180-@)}÷{m/2+m/2}=Lsin@/8Now to calculate final answer .....√Xcm sq + Ycm sq = on simplifying...I.e taking LCM..=L√ 2(1+cos@)/8= L/8×cos (@/2). {1+cos @=2cos sq @/2}

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