A thin rectangular plate with sides of length 'a' and 'b' has mass per unit area varying as `alpha =alpha_(0) ((xy)/(ab))` where `alpha_(0)` is a constant. The co-ordinated of centre of mass of the plate is

A thin rod AB of length a has variable mass per unit length P_(0) (1 + (x)/(a)) where x is the distance measured from A and rho_(0) is a constant. Find the position of centre of mass of the rod.

A thin rod AB of length a has variable mass per unit length rho_(0) (1 + (x)/(a)) where x is the distance measured from A and rho_(0) is a constant. Find the mass M of the rod.

A rod of mass m and length L is non- uniform.The mass of rod per unit length (mu)], varies as "(mu)=bx" ,where b is a constant.The , centre of mass of the ,rod is given by

A rod of length L with sides fully insulated is made of a material whose thermal conductivity K varies with temperature as K=(alpha)/(T) where alpha is constant. The ends of rod are at temperature T_(1) and T_(2)(T_(2)gtT_(1)) Find the rate of heat flow per unit area of rod .

A rod of length L with sides fully insulated is made of a material whose thermal conductivity K varies with temperature as K=(alpha)/(T) where alpha is constant. The ends of rod are at temperature T_(1) and T_(2)(T_(2)gtT_(1)) Find the rate of heat flow per unit area of rod .

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

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

The mass per unit length (lambda) of a non-uniform rod varies linearly with distance x from its one end accrding to the relation, lambda = alpha x , where alpha is a constant. Find the centre of mass as a fraction of its length L.