CBSE Class 11-science Answered

Let's say we want to calculate X_cm , and using integration method it'll be given by,

X_cm = (xλ(x)dx)/(λ(x)dx)

 where λ(x) is the linear mass density which depends upon x coordinate only and it's units are kg/m,

dx = small length element at a distance x m from origin.

The integration is definite and the limits for x are x = 0 to x = L.

In the same manner it can be extended to two or three dimentional objects but the integration changes to area i.e. double integration and volume i.e. triple integration respectively.

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