Question

A glass plate of length $10cm$, breadth $1.54cm$ and thickness $0.20cm$ weight $8.2g$ 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$=7.3\times {10}^{-2}N/m$ and $g=9.8m{s}^{-12}$.

Answer 1

Weight of the glass plate in air $W=8.2\times {10}^{-3}\times 9.8=8.04\times {10}^{-2}$ $kgwt$ (downwards)

Volume of glass plate immersed in water $V=10\times 0.2\times 0.77=1.54c{m}^3=1.54\times {10}^{-6}{m}^3$

Buoyancy force $B=\rho g\left(V\right)=1000\times \left(9.8\right)\times (1.54\times {10}^{-6})=1.51\times {10}^{-2}$ $kgwt$ (upwards)

Force due to surface tension $F_s=T\left[2\right(10+0.2)\times {10}^{-2}]=7.3\times {10}^{-3}\times 20.4\times {10}^{-2}=1.49\times {10}^{-2}$ $kgwt$ (downwards)

Apparent weight of the plate $W^{\prime }=(8.04+1.49-1.51)\times {10}^{-2}=8.02\times {10}^{-2}$ $kgwt$ (downwards)