A circular ring has inner and outer radii equal to `10 mm and 30 mm` respectively Mass of the ring is `m = 0.7` g. It gently pulled out vertically from a water surface by a sensitive spring. When the spring is stretched `3.4 cm` from its equilibrium position the ring is on verge of being pulled out from the water surface. If spring constant is `k = 0.7 Nm^(–1)` find the surface tension of water.

Options

A. `0.02 N//m`
B. `0.07 N//m`
C. `0.04 N//m`
D. `0.09 N//m`

Answer

B

Explanation

When the ring is about to leave the water surface, surface tension force on it is
`F_(ST) = 2piRT + 2pirT = 2pi (R + r)T `
Spring force `F_(s) = kx`
`:. kx = 2pi(R+r)T + mg`
`:. T = (kx - mg)/(2pi(R + r)) = (0.73 xx 3.4 xx 10^(-2)-7 xx 10^(-4) xx 9.8)/(2xx 3.14 xx(30 + 10 xx 10^(-3))) =`
`0.076 Nm^(-1)`