A ring cut with an inner radius 4.85 cm and outer radius 4.95 cm is supported horizontally from one of the pans of a balance so that it comes in contact with the water in a vessel. If surface tension of water is `70 xx 10^(-3) " Nm"^(-1)`, then the extra mass in the other pan required to pull the ring away from water is

Options

A. 2 g
B. 3 g
C. 4.4 g
D. 15 g

Answer

C

Explanation

Given, `r_1 = 4.85 "cm", r_2 = 4.95 "cm" and T= 70 xx 10^(-3) "Nm"^(-1)`
Here, mg = force due to surface tension
`mg = 2pi (r_1 + r_2) xx T`
`m = (2pi (r_1 + r_2) xx T)/( g)`
`m = (2 xx 3.14 xx (4.85 xx 4.95) xx (10^(-2) ) xx 70 xx 10^(-3) )/( 9.8 ) `
`m= (2 xx 3.14 xx 9.8 xx 10^(-2) xx 70 xx 10^(-3) )/( 9.8)`
`m= 6.28 xx 70 xx 10^(-5) = 439.6 xx 10^(-5) ~= 4.4g`