A 1.5 m cylinder of radius 1.1 cm is made of a complicated mixture materials. Its resistivity depends on the distance x from the left and obeys the formula p(x)=a+bx^2, where a and b are constants. At the left, the resistivity is 2.25*10^-8 ohms*m, while at the right end its 8.5*10^-8 ohms*m

a)What is the resistance of the rod?
b)what is the electric field at its midpoint if it carries a 1.75-A current?
c) If we cut the rod into two 75-cm halves, what is the resistance of each half?

a)μΩ

b)

c)Ω

here * stand for multiplication

Explanation:

length of cylinder = 1.5 m

radius of cylinder  =  1.1 cm

resistivity depends on the distance x from the left

............(i)

using equation

let dR is the resistance of thickness dx

where p(x) is resistivity  l is length

a is area

.........................(2)

after integration

 ...............(3)

it is given Ωm

 = Ωm

(here * stand for multiplication )

on solving we get

Ωm

put each value of a  and b and r value in equation 3rd we get

Ω

μΩ

FOR (b)

for mid point  x = L/2

E = p(x)L

for x = L/2

for given current  I = 1.75 A

so electric field

by substitute the values

we get;

(here * stand for multiplication )

c ).

75 cm means length will be half

 that is   x =  L/2

integrate  the second equation with upper limit  L/2  

Let resistance is

so after integration we get

substitute the value of a , b and L we get

Ω

for second half resistance

Ω

(here * stand for multiplication )

because if the tool that you are using is not balanced it there would be false mass.