Question

The linear density of a rod of length 4 m is given by rho(x) measured in kilograms per meter, where x is measured in meters from one end of the rod. rho(x) = 10 + 2 sqrt(x) Find the total mass m of the rod.

Answer 1

Answer:

50.67

Explanation:

L = 4 m

$\rho (x)=10+2\sqrt{x}$

Let the mass of small length dx is dm.

So, dm = ρ(x) dx

Integrate on both the sides within proper limits

$\int dm = \int \rho (x)dx=\int_{0}^{4}\left (10+2\sqrt{x} \right )dx$

$m = \left [ 10x+\frac{4}{3}x^{\frac{3}{2}} \right ]_{0}^{4}$

m = 40 + 32 / 3 = 152  / 3 = 50.67