Embibe Experts Solutions for Chapter: Properties of Solid and Liquid, Exercise 1: Level 1

A metal wire $1 \mathrm{cm}$ in diameter breaks, if the tension in it exceeds $500 \mathrm{N}$. The maximum tension that may be given to similar rope of diameter $4 \mathrm{cm}$ is $4000x \mathrm{N}$. Find the value of $x$.

Young's modulus of steel is $2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}.$ A steel wire has a length of $1 \mathrm{m}$ and area of cross-section $1 {\mathrm{mm}}^2.$ The work required in millijoule to increase its length by $1 \mathrm{mm}$ is :-

A metallic sphere floats in an immiscible mixture of water and a liquid $\left({\rho }_L=13.5\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}\right)$ with $\frac{1}{5}$ portion by volume in the liquid. The density of the metal is $n\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. The value of $n$ is

In a test experiment on a model aeroplane in a wind tunnel the flow speeds on the lower and upper surfaces of the wing are $v$ and $\sqrt{2}v$ respectively. If the density of air is $\rho$ and the surface area of the wing is $A\mathit{,}$ the dynamic lift on the wings is given by $\frac{1}{K}\rho v^{2}A.$ Find $K\mathit{.}$

If the surface tension of a soap solution is $\sigma ,$ The work done in blowing soap bubble of radius $r$ is $K$ times $\mathrm{\pi }{r}^2\sigma$. Determine the value of $K$.

The work done in blowing a soap bubble of $10 \mathrm{cm}$ radius is $($surface tension of the soap solution is $\frac{3}{\mathrm{100}} \mathrm{N} {\mathrm{m}}^{-1}$​$)$

The radii of two soap bubbles are $r_1$ and $r_2$. In isothermal conditions, two meet together in a vacuum. Then the radius of the resultant bubble is given by:

A massless metal plate is placed on a horizontal tabletop lubricated with oil. The sheet is a square of side length $\ell =1.0 \mathrm{m}$ and the oil layer has thickness $\mathrm{h}=1.0 \mathrm{mm}$. Initially one edge of the sheet coincides with one edge of the table. The sheet is pulled outwards without rotation with a constant force $\mathrm{F}=15 \mathrm{N}$. If coefficient of viscosity of the oil is $\eta =0.2 \mathrm{N}-\mathrm{s}/{\mathrm{m}}^2$, how long (in second) will it take to pull half of the sheet out of the table?