Q116 / 150 · MHT CET 2026 (19 April Shift 2) · Physics
A metal wire of length 'L' and density 'd' floats horizontally on the free surface of water. The maximum radius of the wire does not sink in water is
[ $T$ = surface tension of water , $g$ = gravitational acceleration]
[ $T$ = surface tension of water , $g$ = gravitational acceleration]
- A$\sqrt{\dfrac{2dg}{\pi T}}$
- Correct answerB$\sqrt{\dfrac{2T}{\pi dg}}$
- C$\sqrt{\dfrac{\pi dg}{2T}}$
- D$\sqrt{\dfrac{T}{\pi dg}}$
Solution
Weight of the metal wire acting downwards is $W = \pi r^2 L d g$
Maximum upward force due to surface tension is $F = 2 T L$
For the wire to float without sinking, the maximum upward force must balance the weight of the wire.
$2 T L = \pi r^2 L d g$
$r^2 = \dfrac{2 T}{\pi d g}$
$r = \sqrt{\dfrac{2 T}{\pi d g}}$
Answer: $\sqrt{\dfrac{2T}{\pi dg}}$
Maximum upward force due to surface tension is $F = 2 T L$
For the wire to float without sinking, the maximum upward force must balance the weight of the wire.
$2 T L = \pi r^2 L d g$
$r^2 = \dfrac{2 T}{\pi d g}$
$r = \sqrt{\dfrac{2 T}{\pi d g}}$
Answer: $\sqrt{\dfrac{2T}{\pi dg}}$
Hence, the correct answer is option: 'B'.