Question

A rod of length 35.50 cm has linear density (mass per length) given by λ = 50.0 + 23.0x where x is the distance from one end, and λ is measured in grams/meter. (a) What is its mass? g (b) How far from the x = 0 end is its center of mass? m

Answer 1

Answer:

(a)20.65g

(b)0.19m

Explanation:

(a) The total mass would be it's mass per length multiplied by the total lenght

0.355(50 + 23*0.355) = 20.65 g

(b) The center of mass would be at point c where the mass on the left and on the right of c is the same

Hence the mass on the left side would be half of its total mass which is 20.65/2 = 10.32 g

$c(50 + 23c) = 10.32$

$23c^2 + 50c - 10.32 = 0$

$c \approx 0.19m$