Here, L is the body's height. Stretching the object by a factor of a along the z-axis is equivalent to dividing the mass density by a (meaning ρ ρ ′ ( x , y , z ) = ρ ρ ( x , y , z / a ) / a ), as well as integrating over new limits 0 and a L (the new height of the object), thus leaving the total mass unchanged. This means the new moment of inertia will be: