There is a rod of length `l` , its density varies with length as distance of `lambda=ax` , where `x` is distance from left end. Find center of mass from left end.

The density of a rod of length L varies as rho=A+Bx where x is the distance from the left end. Locate the centre of mass.

The linear density of a thin rod of length 1m lies as lambda = (1+2x) , where x is the distance from its one end. Find the distance of its center of mass from this end.

The liner density of a rod of length 2m varies as lambda = (2 + 3x) kg/m, where x is distance from end A . The distance of a center of mass from the end B will be

Mass is non-uniformly distributed over the rod of length l, its linear mass density varies linearly with length as lamda=kx^(2) . The position of centre of mass (from lighter end) is given by-

Find coordinates of mass center of a non-uniform rod of length L whose linear mass density lambda varies as lambda=a+bx, where x is the distance from the lighter end.

The centre of mass of a non-uniform rod of length L whose mass per unit length lambda is proportional to x^2 , where x is distance from one end

A rod of length L is of non uniform cross-section. Its mass per unit length varies linearly with distance from left end. Then its centre of mass from left end is at a distance. (Take linear density at left end=0).

A thin bar of length L has a mass per unit length lambda , that increases linerarly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is lambda_(0) , then the distance of the centre of mass from the lighter end is

Figure shows a rope of variable mass whose linear mass density is given by , lambda = Ax , where A is + ve constant and x is distance from left end . It bis placed on a smooth horizontal surface . A force F is acting on it as shown . (i) Find total mass of the rope . (ii) Find tension at point P.

A heavy metallic rod of non-uniform mass distribution, is hanged vertically from a rigid support. The linear mass density varies as lambda_((x))=k xx x where x is the distance measured along the length of rod, from its lower end. Find extension in rod due to its own weight.