1
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

An air bubble of negligible weight having radius r rises steadily through a solution of density $$\sigma$$ at speed v. The coefficient of viscosity of the solution is given by :

A
$$\eta = {{4r\sigma g} \over {9v}}$$
B
$$\eta = {{2{r^2}\sigma g} \over {9v}}$$
C
$$\eta = {{2\pi {r^2}\sigma g} \over {9v}}$$
D
$$\eta = {{2{r^2}\sigma g} \over {3\pi v}}$$
2
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1 A wire of length L is hanging from a fixed support. The length changes to L1 and L2 when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to :

A
$$\sqrt {{L_1}{L_2}}$$
B
$${{{L_1} + {L_2}} \over 2}$$
C
$$2{L_1} - {L_2}$$
D
$$3{L_1} - 2{L_2}$$
3
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1 A water drop of radius 1 $$\mu$$m falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 $$\times$$ 10$$-$$5 Nsm$$-$$2 and its density is negligible as compared to that of water 106 gm$$-$$3. Terminal velocity of the water drop is :

(Take acceleration due to gravity = 10 ms$$-$$2)

A
145.4 $$\times$$ 10$$-$$6 ms$$-$$1
B
118.0 $$\times$$ 10$$-$$6 ms$$-$$1
C
132.6 $$\times$$ 10$$-$$6 ms$$-$$1
D
123.4 $$\times$$ 10$$-$$6 ms$$-$$1
4
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1 Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.

Reason R : Coefficient of viscosity = $${{Force} \over {Velocity\,gradient}}$$

Choose the correct answer from the options given below :

A
Both A and R are true, and R is the correct explanation of A.
B
Both A and R are true but R is NOT the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
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