The centre of mass of a non uniform rod of length L, whose mass per unit length varies as `rho=(k.x^2)/(L)` where k is a constant and x is the distance of any point from one end is (from the same end)

Options

A. `(3)/(4) L`
B. `(1)/(4) L`
C. `(k)/(L)`
D. `(3 k)/(L)`

Answer

A

Explanation

(a) `:. x_(cm) = (int_0^L (K)/(L) x^2 dx.x)/(int_0^L (K)/(L) x^2 dx) = ((x^(4))/(4)|_(0)^(L))/((x^(3))/(3)|_(0)^(L))=(3)/(4)L`
.