1
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
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 103 kg m−3 , 0.07 Nm−1 and 10 ms−2 , respectively, the value of h (in mm) is _________.
2
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate (KMnO4) of different concentrations n1 and n2 (n1 > n2) molecules per unit volume with $$\Delta$$n = (n1 − n2) << n1. When they are connected by a tube of small length l and cross-sectional area S, KMnO4 starts to diffuse from the left to the right vessel through the tube. Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion. The speed v of the molecules is limited by the viscous force −$$\beta$$v on each molecule, where $$\beta$$ is a constant. Neglecting all terms of the order ($$\Delta$$n)2, which of the following is/are correct? (kB is the Boltzmann constant)
A
the force causing the molecules to move across the tube is $$\Delta n{k_b}TS$$
B
force balance implies $${n_1}\beta vl = \Delta n{k_B}T$$
C
total number of molecules going across the
tube per sec is $$\left( {{{\Delta n} \over l}} \right)\left( {{{{k_B}T} \over \beta }} \right)S$$
D
rate of molecules getting transferred through the tube does not change with time
3
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
A circular disc of radius R carries surface charge density
$$\sigma \left( r \right) = {\sigma _0}\left( {1 - {r \over R}} \right)$$, where $$\sigma$$0 is a constant and r is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is $$\phi$$0. Electric flux through another spherical surface of radius $${R \over 4}$$ and concentric with the disc is $$\phi$$. Then the ratio $${{{\phi _0}} \over \phi }$$ is ________.
4
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________.