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प्रश्न
The mass per unit length of a non-uniform rod of length L varies as m = λx where λ is constant. The centre of mass of the rod will be at ______.
पर्याय
`2/3`L
`3/2`L
`1/2`L
`4/3`L
MCQ
रिकाम्या जागा भरा
उत्तर
The mass per unit length of a non-uniform rod of length L varies as m = λx where λ is constant. The centre of mass of the rod will be at `underlinebb(2/3"L")`.
Explanation:
`"X"_"cm"=int_0^"L"(("dm")x)/(int_0^"L"("dm"))`
= `(int_0^"L"(lambdax"d"x)x)/(int_0^"L"(lambdax"d"x))`
= `(2"L")/3`
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