A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is V0. A hole with a small area $$\alpha $$4$$\pi $$R2($$\alpha $$ << 1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?
A
The ratio of the potential at the center of the shell of that of the point at $${1 \over 2}$$R from center towards the hole will be $${{1 - \alpha } \over {1 - 2\alpha }}$$.
B
The potential at the center of the shell is reduced by 2$$\alpha $$V0.
C
The magnitude of electric field at the center of the shell is reduced by $${{\alpha {V_0}} \over {2R}}$$.
D
The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance 2R from the center of the spherical shell will be reduced by $${{\alpha {V_0}} \over {2R}}$$.
2
JEE Advanced 2019 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Consider a spherical gaseous cloud of mass density $$\rho $$(r) in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy K. The force acting on the particles is their mutual gravitational force. If $$\rho $$(r) is constant in time, the particle number density n(r) = $$\rho $$(r)/m is [G is universal gravitational constant]
A
$${K \over {6\pi {r^2}{m^2}G}}$$
B
$${K \over {\pi {r^2}{m^2}G}}$$
C
$${3K \over {\pi {r^2}{m^2}G}}$$
D
$${K \over {2\pi {r^2}{m^2}G}}$$
3
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T1 and T2 of different materials having water contact angles of 0$$^\circ $$ and 60$$^\circ $$, 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 N/m, density of water = 1000 kg/m3, take g = 10 m/s2]
A
For case I, if the joint is kept at 8 cm above the water surface, the height of water colomn in the tube will be 7.5 cm. (Neglect the weight of the water in the meniscus).
B
For case I, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be more than 8.75 cm. (Neglect the weight of the water in the meniscus).
C
The correction in the height of water column raised in the tube, due to weight of water contained in the meniscus, will be different for both cases.
D
For case II, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be 3.75 cm. (Neglect the weight of the water in the meniscus).
4
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A conducting wire of parabolic shape, initially y = x2, is moving with velocity $$v = {v_0}\widehat i$$ in a non-uniform magnetic field $$B = {B_0}\left( {1 + {{\left( {{y \over L}} \right)}^\beta }} \right)\widehat k$$, as shown in figure. If V0, B0, L and $$\beta $$ are positive constants and $$\Delta $$$$\phi $$ is the potential difference developed between the ends of the wire, then the correct statement(s) is/are
