Embibe Experts Solutions for Chapter: Mechanics of Solids and Fluids, Exercise 1: BITSAT 2017

Two separate soap bubbles of radii $3\times {10}^{-3} \mathrm{m}$ and $2\times {10}^{-3} \mathrm{m}$ respectively, formed of same liquid (surface tension $65\times {10}^{-2} \mathrm{N} {\mathrm{m}}^{-1}$) come together to form a double bubble. The radius of interface of double bubble is

A steel wire of cross-sectional area $4 {\mathrm{cm}}^2$ has elastic limit of $2.2\times {10}^8 \mathrm{N} {\mathrm{m}}^{-2}$. The maximum upward acceleration that can be given to a $1000 \mathrm{kg}$ elevator supported by this steel wire if the stress is to exceed one-fourth of the elastic limit is [Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

A rubber cord has a cross-sectional area ${10}^{-6} {\mathrm{m}}^2$ and total unstretched length $0.1 \mathrm{m}$. It is stretched to $0.125 \mathrm{m}$ and then released to project a particle of mass $5.0 \mathrm{g}$. The velocity of projection is [Given, Young's modulus of rubber, $Y=5\times {10}^8 \mathrm{N} {\mathrm{m}}^{-2}$]

A block of wood floats in water with $(4/5{)}^{\mathrm{th}}$ of its volume submerged. If the same block just floats in a liquid, the density of liquid in $\left(\mathrm{kg} {\mathrm{m}}^{-3}\right)$ is

Breaking stress of a steel wire is $p$ and the density of steel is $\rho$. The greatest length of steel wire that can hang vertically without breaking is

If a drop of liquid breaks into smaller droplets, it results in lowering of temperature of the droplets. Let a drop of radius $R$, break into $N$ small droplets each of radius $r$, then decrease (drop) in temperature $Q$ (given, specific heat of liquid drop$=S$ and surface tension $=T$ )

An ice-berg of density $900 \mathrm{kg} {\mathrm{m}}^{-3}$ is floating in water of density $1000 \mathrm{kg} {\mathrm{m}}^{-3}$. The percentage of volume of ice-berg outside the water is 

Work done in increasing the size of a soap bubble from radius of ($3$ to $5$) $\mathrm{cm}$ is nearly (surface tension of soap solution $=0.03 \mathrm{N} {\mathrm{m}}^{-1}$)