Question:
A leak proof cylinder of length $1 \mathrm{~m}$, made of a metal which has very low coefficient of expansion is floating vertically in water at $0^{\circ} \mathrm{C}$ such that its height above the water surface is $20 \mathrm{~cm}$. When the temperature of water is increased to $4^{\circ} \mathrm{C}$, the height of the cylinder above the water surface becomes $21 \mathrm{~cm}$. The density of water at $T=4^{\circ} \mathrm{C}$, relative to the density at $T=0^{\circ} \mathrm{C}$ is close to:
$1.26$
$1.04$
$1.01$
$1.03$
Question of from chapter.
JEE Main Previous Year 8.Jan 2020
Correct Option: 3
Solution:
Download now India’s Best Exam Preparation App
Class 9-10, JEE & NEET
Related Questions
A hollow spherical shell at outer radius $R$ floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ wr.t water, the value of $r$ is :
An air bubble of radius $1 \mathrm{~cm}$ in water has an upward acceleration $9.8 \mathrm{~cm} \mathrm{~s}^{-2}$. The density of water is $1 \mathrm{gm}$ $\mathrm{cm}^{-3}$ and water offers negligible drag force on the bubble. The mass of the bubble is $\left(\mathrm{g}=980 \mathrm{~cm} / \mathrm{s}^{2}\right)$
Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density $d$. The area of the base of both vessels is $S$ but the height of liquid in one vessel is $x_{1}$ and in the other, $x_{2}$. When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is:
Consider a solid sphere of radius $R$ and mass density $\rho(r)=\rho_{0}\left(1-\frac{r^{2}}{R^{2}}\right), 0<r \leq R$. The minimum density of a liquid in which it will float is:
Two liquids of densities $\rho_{1}$ and $\rho_{2}\left(\rho_{2}=2 \rho_{1}\right)$ are filled up behind a square wall of side $10 \mathrm{~m}$ as shown in figure. Each liquid has a height of $5 \mathrm{~m}$. The ratio of the forces due to these liquids exerted on upper part $M N$ to that at the lower part $N O$ is (Assume that the liquids are not mixing):
A cubical block of side $0.5 \mathrm{~m}$ floats on water with $30 \%$ of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take, density of water $=10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ ]
A submarine experiences a pressure of $5.05 \times 10^{6} \mathrm{~Pa}$ at depth of $d_{1}$ in a sea. When it goes further to a depth of $d_{2}$, it experiences a pressure of $8.08 \times 10^{6} \mathrm{~Pa}$. Then $d_{1}-d_{1}$ is approximately (density of water $=10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ and acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ ):
A wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When certain amount of an oil poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is:
A load of mass $M \mathrm{~kg}$ is suspended from a steel wire of length $2 \mathrm{~m}$ and radius $1.0 \mathrm{~mm}$ in Searle’s apparatus experiment. The increase in length produced in the wire is $4.0 \mathrm{~mm}$. Now the load is fully immersed in a liquid of relative density 2 . The relative density of the material of load is 8 . The new value of increase in length of the steel wire is :
A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by:
