Question

A hollow cylindrical copper pipe is 1.50 m long and has an outside diameter of 3.50 cm and an inside diameter of 2.50 cm. How much does it weigh?

Short answer

Weight of hollow cylinder copper pipe is 61.7N

Step-by-step solution

Identification of given data

Length of hollow cylindrical copper pipe = 1.50 m

Outer diameter of cylindrical copper pipe = 3.50cm =$3.50\times {10}^{-2}m$

Inner diameter of cylindrical pipe = 2.50 cm =$2.50\times {10}^{-2}m$

Concept of density and weight

Density is ratio of mass of object and volume of object.

In other words, the mass of a fluid per unit volume is its definition.

$\rho =\frac{m}{V}$…………… (i)

Weight is defined as product of mass and acceleration due to gravity.

How much an item weighs for a given volume is determined by its density.

W = mg…………. (ii)

Determination of weight of hollow cylindrical copper pipe

Volume of hollow cylindrical copper pipe,

$V=\pi \left(R_2^2-R_1^2\right)L$

Here,$R_2$is outer radius.

$R_1$ is inner radius.

L is length of hollow cylinder.

Substitute values in above equation,

$V=\pi \left[{\left(1.75\times {10}^{-2}\right)}^2-{\left(1.25\times {10}^{-2}\right)}^2\right]\left(1.50\mathrm{m}\right)=7.06\times {10}^{-4}{\mathrm{m}}^3$

Mass of hollow cylinder can be found by using equation(i),

m = pV

Substitute value in above equation we get,

$m=\left(8.9\times {10}^3\mathrm{kg}/{\mathrm{m}}^3\right)\left(7.06\times {10}^{-4}{\mathrm{m}}^3\right)=6.29\mathrm{kg}$

Weight can be found by using equation(ii),

W = mg

Substitute value in above equation we get,

$W=\left(6.29\mathrm{kg}\right)\left(9.81\mathrm{m}/{\mathrm{s}}^2\right)=61.7\mathrm{N}$

Thus, weight of the hollow cylinder is 61.7N