If linear charge density of a wire of length L depends on distance x from one end as `lambda=(lambda_(0)(x))/(L` .Find total charge of wire :-

the linear charge density of a thin metallic rod varies with the distance x from the end as lambda=lambda_(0)x^(2)(0 le x lel) The total charge on the rod is

The linear mass density of a rod of length 2L varies with distance (x) from center as lambda=lambda_(0)(1+(x)/(L)) .The distance of COM from center is nL.Then n is

[" A wire of length "L" is placed along "x" &axis "],[" with one end at the origin.The linear charge "],[" density of the wire varies with "],[" Q."" distance "x" from the origin as "lambda=lambda_(0)((x^(3))/(L))" ."],[" Where "varnothing_(0)" is a positive constant.The total "],[" charge "Q" on the rod is "]

The density of a thin rod of length l varies with the distance x from one end as rho=rho_0(x^2)/(l^2) . Find the position of centre of mass of rod.

The linear mass density of a thin rod AB of length L varies from A to B as lambda (x) =lambda_0 (1 + x/L) . Where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicualr to the rod is :

A semicircular wire is uniformly charged with linear charge density dependent on the angle theta from y -direction as lambda=lambda_(0) |sin theta| , where lambda_(0) is a constant. The electric field intensity at the centre of the arc is