Embibe Experts Solutions for Chapter: Properties of Solid and Liquid, Exercise 1: JEE Advanced Paper 2 - 2014

A cubical solid aluminum $\left(\mathrm{bulk} \mathrm{modulus}=-V\frac{\mathrm{d}P}{\mathrm{d}V}=70 \mathrm{GPa}\right)$ block has an edge length of $1 \mathrm{m}$ on the surface of the earth. It is kept on the floor of a $5 \mathrm{km}$ deep ocean. Taking the average density of water and the acceleration due to gravity to be ${10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ and $10 \mathrm{m} {\mathrm{s}}^{-2}$, respectively, the change in the edge length of the block in $\mathrm{mm}$ is ________.

Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_0$. Which of the following statements is (are) true?

A steel wire of diameter $0.5 \mathrm{mm}$ and Young's modulus $2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ carries a load of mass $M$. The length of the wire with the load is $1.0 \mathrm{m}$. A vernier scale with $10$ divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count $1.0 \mathrm{mm}$, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by $1.2 \mathrm{kg}$, the vernier scale division which coincides with a main scale division is __________. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2} \text{and} \mathrm{\pi }= 3.2$.

A cylindrical tube, with its base as shown in the figure., is filled with water. It is moving down with a constant acceleration $a$ along a fixed inclined plane with angle $\theta =45°$. $P_1$ and $P_2$ are pressures at point $1$ and $2$, respectively, located at the base of the tube. Let $\beta =\frac{\left(P_1-P_2\right)}{\left(\rho gd\right)}$, where $\rho$ is density of water, $d$ is the inner diameter of the tube and $g$ is the acceleration due to gravity. Which of the following statement(s) is (are) correct?

An open-ended U-tube of uniform cross-sectional area contains water (density ${10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ ). Initially the water level stands at $0.29 \mathrm{m}$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800 \mathrm{kg} {\mathrm{m}}^{-3}$ is added to the left arm until its length is $0.1 \mathrm{m}$, as shown in the schematic figure below. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is

When water is filled carefully in a glass, one can fill it to a height $h$ above the rim of the glass due to the surface tension of water. To calculate $h$ just before water starts flowing, model the shape of the water above the rim as a disc of thickness $h$ having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the rim and water starts flowing from there. If the density of water, its surface tension and the acceleration due to gravity are ${10}^3 \mathrm{kg} {\mathrm{m}}^{-3},0.07 \mathrm{N} {\mathrm{m}}^{-1}$ and $10 \mathrm{m} {\mathrm{s}}^{-2}$ respectively, the value of $h$ (in $\mathrm{mm}$) is ________.

A cylindrical capillary tube of $0.2\mathrm{ }\mathrm{m}\mathrm{m}$ radius is made by joining two capillaries ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ of different materials having water contact angles of $0^{\mathrm{o}}$ and ${60}^{\mathrm{o}},$ respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in figure. Which of the following option(s) is(are) correct?

(Surface tension of water $=0.075\mathrm{ }\mathrm{N} {\mathrm{m}}^{-1}$, density of water $=1000\mathrm{ }\mathrm{k}\mathrm{g} {\mathrm{m}}^{-3},$ take $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2})$

A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$ . The angle of contact between water and the wall of the capillary tube is $\theta$ . Ignore the mass of water in the meniscus. Which of the following statements is (are) true?