A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as $$T(t) = {T_0}\left( {1 + \beta {t^{{1 \over 4}}}} \right)$$, where $$\beta $$ is a constant with appropriate dimension while T0 is a constant with dimension of temperature. The heat capacity of the metal is
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 $${{\alpha {V_0}} \over {2R}}$$.
3
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
$${K \over {2\pi {r^2}{m^2}G}}$$
4
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).
