Question

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 ______.

Options

• `2/3`L

• `3/2`L

• `1/2`L

• `4/3`L

Answer 1

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`