The length of the wire increases 8 mm when a weight of 5 kg is hung. If all conditions are same, but the radius of the wire is doubled, what will be the decrease in its length ?

Options

A. 2 mm
B. 1 mm
C. 0.5 mm
D. 1.5 mm

Answer

A

Explanation

` Y = ( mgL ) /( pi r ^ 2 l ) `
Now, we have ` l prop (1 ) /( r ^ 2 ) `
Hence, when radius of wire is doubld the elongation decreases to one - fourth.
So, ` l = ( 1 ) /( 4 ) xx 8 ` mm = 2 mm