A wire of length `L` metres, made of a material of specific gravity 8 is floating horizontally on the surface of water. If it is not wet by water, the maximum diameter of the wire (in mm) upto which it can continue to float is (surface tension of water is `T=70xx10^(-3)Nm^(-1)`)

Options

A. 0.75 mm
B. 1.5 mm
C. 1.5 cm
D. 1.5 m

Answer

B

Explanation

F= 2l
mg= 2T l
`rho pi r^(2) Lg = 2 TL`
`r^(2) = (2TL)/(rhopiLG) = (2T)/(rho pi g)`
` r = sqrt((2T)/(rho pi g))`
` d = 2r = 2 sqrt((2xx70)/(8xx22/7xx980))`
` = 2 xx 7 sqrt((1)/(4xx22xx49xx2))`
` = 2/2 sqrt(1/44)=sqrt(0.022)`
` d = sqrt(2.2xx10^(-2))= 1.5 xx10^(-1)` cm
d = 1.5 mm.