Embibe Experts Solutions for Chapter: Properties of Solid and Liquid, Exercise 1: JEE Main - 10th January 2019 Shift 1

A force is applied to a steel wire $A$, rigidly clamped at one end. As a result elongation in the wire is $0.2 \mathrm{mm}$. If same force is applied to another steel wire $B$ of double the length and a diameter $2.4$ times that of the wire $A$, the elongation in the wire $B$ will be (wires having uniform circular cross sections)

If $1000$ droplets of water of surface tension $0.07 \mathrm{N} {\mathrm{m}}^{-1}$. having same radius $1 \mathrm{mm}$ each, combine to from a single drop. In the process the released surface energy is-

$\left(\text{Take} \mathrm{\pi }=\frac{22}{7}\right)$

A thin rod having a length of $1 \mathrm{m}$ and area of cross-section $3\times {10}^{-6} {\mathrm{m}}^2$ is suspended vertically from one end. The rod is cooled from $210°\mathrm{C}$ to $160°\mathrm{C}$. After cooling, a mass $M$ is attached at the lower end of the rod such that the length of rod again becomes $1 \mathrm{m}$. Young's modulus and coefficient of linear expansion of the rod are $2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ and $2\times {10}^{-5} {\mathrm{K}}^{-1}$, respectively. The value of $M$ is ______ $\mathrm{kg}$. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Under the same load, wire A having length $5.0 \mathrm{m}$ and cross section $2.5\times {10}^{-5} {\mathrm{m}}^2$ stretches uniformly by the same amount as another wire $B$ of length $6.0 \mathrm{m}$ and a cross section of $3.0\times {10}^{-5} {\mathrm{m}}^2$ stretches. The ratio of the Young's modulus of wire $A$ to that of wire $B$ will be:

A mercury drop of radius ${10}^{–3} \mathrm{m}$ is broken into $125$ equal size droplets. Surface tension of mercury is $0.45 \mathrm{N} {\mathrm{m}}^{–1}$ . The gain in surface energy is:

A certain pressure '$P$' is applied to $1$ litre of water and $2$ litre of a liquid separately. Water gets compressed to $0.01\%$ whereas the liquid gets compressed to $0.03\%$. The ratio of Bulk modulus of water to that of the liquid is $\frac{3}{x}$. The value of $x$ is ______.

The Young's modulus of a steel wire of length $6 \mathrm{m}$ and cross-sectional area $3 {\mathrm{mm}}^2$, is $2 \times {11}^{11} \mathrm{N}/{\mathrm{m}}^2$ . The wire is suspended from its support on a given planet. A block of mass $4 \mathrm{kg}$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the earth. The elongation of wire is (Take $g$ on the earth $= 10 \mathrm{m}/{\mathrm{s}}^2$ ):

The surface of water in a water tank of cross section area $750 {\mathrm{cm}}^2$ on the top of a house is $h \mathrm{m}$. above the tap level. The speed of water coming out through the tap of cross section area $500 {\mathrm{mm}}^2$ is $30 \mathrm{cm} {\mathrm{s}}^{-1}$. At that instant, $\frac{\mathrm{d}h}{\mathrm{d}t}$ is $x\times {10}^{-3} \mathrm{m} {\mathrm{s}}^{-1}$. The value of $x$ will be ______.