Streamline flow is more likely for liquids with
Is viscosity a vector?
Viscosity is a property of liquid it does not have any direction, hence it is a scalar quantity.
Is surface tension a vector?
No, surface tension is a scalar quantity.
Surface tension $=\frac{\text { Work done }}{\text { Surface area }}$, where work done and surface area both are scalar quantities.
Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged, if the density of ice is $\rho_i=0.917 \mathrm{~g} \mathrm{~cm}^{-3} ?$
Given, density of ice $\left(\rho_{\text {ice }}\right)=0.917 \mathrm{~g} / \mathrm{cm}^3$
Density of water $\left(\rho_w\right)=1 \mathrm{~g} / \mathrm{cm}^3$
Let $V$ be the total volume of the iceberg and $V^{\prime}$ of its volume be submerged in water.
In floating condition.
Weight of the iceberg = Weight of the water displaced by the submerged part by ice
$$V_{\rho_{\text {ice }}} g=V^{\prime} \rho_w g$$
or $$\frac{V^{\prime}}{V}=\frac{\rho_{c e}}{\rho_w}=\frac{0.917}{1}=0.917 \quad(\because \text { Weight }=m g=v \rho g)$$
A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass $M$ and density $\rho$ is suspended by a massless spring of spring constant $k$. This block is submerged inside into the water in the vessel. What is the reading of the scale?
Consider the diagram,
The scale is adjusted to zero, therefore, when the block suspended to a spring is immersed in water, then the reading of the scale will be equal to the thrust on the block due to water.
$$\begin{aligned} \text { Thrust } & =\text { weight of water displaced } \\ & =V_\rho g \text { (where } V \text { is volume of the block and } \rho_w \text { is density of water) } \\ & =\frac{m}{\rho} \rho_w g=\left(\frac{\rho_w}{\rho}\right) m g \end{aligned}$$
$$\left(\because \text { Density of the block } \rho=\frac{\text { mass }}{\text { volume }}=\frac{m}{V}\right)$$
