Question

Find the maximum possible mass of a greased needle floating on water surface. $T$ is the surface tension of water , $l$ is the length of the needle:

• A. $m_{max}=\frac{2Tl}{g}$
• B. $m_{max}=\frac{g}{2Tl}$
• C. $m_{max}=\frac{2Tg}{l}$
• D. $m_{max}=\frac{Tl}{g}$

Answer 1

The correct option is A $m_{max}=\frac{2Tl}{g}$

Lets consider, $T=$ surface tension

$F=$ Force due to surface tension

$l=$ length of the needle

For floating

Upward force $=$ Downward force

$2Fcos\theta =mg$. . . . .(1)

and the force due to the surface tension is given by

$F=Tl$

Equation (1) becomes.

$2Tlcos\theta =mg$

$m=\frac{2Tlcos\theta }{g}$

for maximum, $cos\theta =1$

$m_{max}=\frac{2Tl}{g}$

The correct option is A.