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).
2
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Consider a thin square plate floating on a viscous liquid in a large tank. The height $$h$$ of the liquid in the tank is much less than the width of the tank. The floating place is pulled horizontally with a constant velocity $${\mu _{0.}}$$ Which of the following statements is (are) true?
A
The resistive force of liquid on the plate is inversely proportional to $$h$$
B
The resistive force of liquid on the plate is independent of the area of the plate
C
The tangential (shear) stress on the floor of the tank increases with $${\mu _0}$$
D
The tangential (shear) stress on the plate varies linearly with the viscosity $$\eta $$ of the liquid
3
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
A uniform capillary tube of inner radius $$r$$ is dipped vertically into a beaker filled with water. The water rises to a height $$h$$ in the capillary tube above the water surface in the beaker. The surface tension of water is $$\sigma .$$ The angle of contact between water and the wall of the capillary tube is $$\theta .$$ Ignore the mass of water in the meniscus. Which of the following statements is (are) true?
A
For a given material of the capillary tube, $$h$$ decreases with increase in $$r$$
B
For a given material of the capillary tube, $$h$$ is independent of $$\sigma $$
C
If this experiment is performed in a lift going up with a constant acceleration, then $$h$$ decreases
D
$$h$$ is proportional to contact angle $$\theta $$
4
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
A human body has a surface area of approximately $$1\,m{}^2.$$ The normal body temperature is $$10$$ $$K$$ above the surrounding room temperature $${T_0}.$$ Take the room temperature to be $${T_0} = 300K.$$ For $${T_0} = 300\,K,$$ the value of $$\sigma T_0^4 = 460\,W{m^{ - 2}}$$ (where $$\sigma $$ is the Stefan-Boltzmann constant).
Which of the following options is / are correct?
A
The amount of energy radiated by the body in $$1$$ second is close to $$60$$ joules
B
If the surrounding temperature reduces by a small amount $$\Delta {T_0} < < {T_0},$$ then to maintain the same body temperature the same (living) human being needs to radiate $$\Delta W = 4\sigma T_0^3\Delta {T_0}$$ more energy per unit time
C
Reducing the exposed surface area of the body (e.g. by curling up) allows human to maintain the same body temperature while reducing the energy lost by radiation
D
If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths
