A Copper wire has a resistance of 0.5 ohm.Another copper wire of the same mass as the first one is double in length of the first.Find the resistance of the second wire.

Mass of the copper wire is same. 

M1 = M2

d*pi*r1^2*l1 = d*pi*r2^2*l2 (where d is the density of copper, r1 and r2 are the radius of 2 wires, l1 and l2 is their lengths)

 

Now, l2 = 2l1

Hence, d*pi*r1^2*l1 = d*pi*r2^2*2l1

 r1^2 = 2r2^2

r2^2 = r1^2/2

 

For first wire, Resistance = rho*l1/A1

0.5 = rho*l1/pi*r1^2 

 

For second wire, resistance =  rho*l2/A2

= rho*l2/pi*r2^2 

= rho*2l1/pi(r1^2/2)

= 4( rho*l1/pi*r1^2 )

= 4*0.5

= 2 ohm