A glass plate of length `10 cm`, breadth `1.54 cm` and thickness `0.20 cm` weigh `8.2 g` in air. It is held vertically with the long side horizontal and the lower half under water. Find the apparent weight of the plate. Surface tension of water `=7.3xx10^(-2)N//m` and `=9.8ms^(-12)`

Options

A. `40.16xx10^-3N`
B. `80.16xx10^-3N`
C. `30.12xx10^-3N`
D. `25.15xx10^-3N`

Answer

B

Explanation

The forces acting on the plate are
(i) `mg(darr)`
(ii) force due to surface tension `(F_T)(darr)`
(iii) Buoyant force `(B_F)(uarr)`
`W=mg=(8.2xx10^-3)xx9.8=80.36xx10^-3N`
The water is in contact along the length,
`L=2(10+0.2)=20.4cm`
`F_T=(20.4xx10^-2)(7.3xx10^-2)=148.92xx10^-4N`
`B_F=[(10xx0.2xx1.54)/(2)xx10^-6]xx1000xx9.8`
`=15.092xx10^-3N`
Apparent weight
`w+F_T+B_F=(80.36+14.892-15.092)xx10^-3`
`=80.16xx10^-3N`