R P Goyal and S P Tripathi Solutions for Chapter: Upthrust in Fluids, Archimedes' Principle and Floatation, Exercise 1: EXERCISE–5(A)

A body experiences an upthrust $F_1$ in river water and $F_2$ in sea water when dipped up to the same level. Which is more $F_1$ or $F_2$? Give reason. 

A small block of wood is held completely immersed in (i) water, (ii) glycerine and then released. In each case, what do you observe? Explain the difference in your observation in the two cases.

A body held completely immersed inside a liquid experiences two forces. $F_1$ the force due to gravity and $F_2$, the buoyant force. Draw a diagram showing the direction of these forces acting on the body and state the conditions when the body will float or sink. 

Prove that the loss in weight of a body when immersed wholly or partially in a liquid is equal to the buoyant force (or upthrust) and this loss is because of the difference in pressure exerted by liquid on the upper and lower surfaces of the submerged part of the body.

Describe an experiment to verify Archimedes' principle.

A solid of density $5000 {\mathrm{kgm}}^{-3}$ weighs $0.5 \mathrm{kg}$  in air. It is completely immersed in a liquid of density $800 {\mathrm{kgm}}^{-3}$. Calculate the apparent weight (in $\mathrm{kgf}$) of the solid in the liquid.

A metal cube of edge $5 \mathrm{cm}$ and density $9 \mathrm{g} {\mathrm{cm}}^{-3}$ is suspended by a thread so as to be completely immersed in a liquid of density$1.2 \mathrm{g} {\mathrm{cm}}^{-3}$ . Find the tension in thread. (Take$\mathrm{g} = 10 \mathrm{m} {\mathrm{s}}^{-2}$ ) 

A block of wood is floating on water with its dimensions  $50 \mathrm{cm} \times 50 \mathrm{cm} \times 50 \mathrm{cm}$  inside water. Calculate the buoyant force acting on the block. Take$g = 9.8 \mathrm{N} {\mathrm{kg}}^{-1}$ .