A thin wire is bent into the shape of a semi-circle x^2 + y^2 = 9 (x greater than or equal to 0)?

Question

If the linear density is a constant 'k', find the mass of the wire.

a) 3kπ

b) 9kπ

c) 6kπ

d) kπ

e) (kπ)/6

Answer 1

x^2 + y^2 = 9

Or, x^2 + y^2 = 3^2

Therefore radius r = 3

Perimeter of full circle = 2πr

The wire is in the shape of a semi-circle. Therefore lengths of wire = 2πr/2 = πr = 3π

Mass = length * linear density = 3π * k = 3kπ

Ans: (a)

AI P has used full circle instead of semi-circle.

Answer 2

changing circle to semi-circle

r=3

c=2*pi*r=2*pi*3

mass=6*k*pi

answer: c)

if semi-circle radius=3

length=pi*3

mass=3*k*pi

answer: a)