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)`

Answer

A

Explanation

Volume of the portion of the plate immersed in water is
`10xx(1)/(2)(1.54)xx0.2=1.54cm^(3)`
Therefore, if the density of water is taken as 1, Then uptrust
=weight of the water displaced
`=1.54xx1xx981509.2 dynes`
Now, the total length of the plate in contact with the water surface is `2(10+0.2)=20.4 cm`
`:.` Downward pull upon the plate due to surface tension
`=20.4xx73=1489.2 dynes`
`:.` Resultant upthrust
`=1509.2-1489.2`
`=20.0 dynes=(20)/(980)`
`=0.0204 gm-wt`
`:.` Apparent weight of the plate in water
=weight of the plate in air-resultant uothrust
`=8.2-0.0204=8.1796 gm`.