When a metal sphere is suspended at the end of a metal wire, its extension is 0.4 mm. If another metal sphere of the same material with its radius is half of the previous, is suspended then extension would be

Options

A. 0.05 mm
B. 0.02 mm
C. 0.01 mm
D. 0.32 mm

Answer

A

Explanation

`l_(1) prop m_(1), l_(2) prop m_(2)`
`(l_(2))/(l_(1))=(m_(2))/(m_(1))=(rho v_(2))/(rho v_(1)) =((4pi)/(3) r_(2)^(3))/((4pi)/(3)r_(1)^(3))`
`(l_(2))/(l_(1)) =((r_(2))/(r_(1)))^(3) =(((r )/(2))/(r ))^(3)=(1)/(8)`
`l_(2)=(l_(1))/(8) =(0.4)/(8) =0.05` mm.