Dimensional Analysis

[Moment of force] = [force distance] =

Impulse = force time

Dimensional formula for frequency is

The viscosity of the liquid can be calculated using the formula for the time taken by a spherical ball to sink through a fluid:
where: - is the viscosity,
- is the radius of the ball,
- is the density of the ball,
- is the density of the liquid,
- is the acceleration due to gravity,
- is the velocity of the ball, which is calculated from the time taken to sink.
Using the data provided, we compute the velocity from the given times and then apply the formula. The final result for the coefficient of viscosity is Pa.s.

Step 1: Understanding the Question:
The objective is to derive the dimensional formulas for each physical quantity and match them with the corresponding dimensions given in List-II.
Step 3: Detailed Explanation:
(a) Torque ( ):
Formula: .
Dimensions: .
This matches with (iv).
(b) Gravitational constant (G):
Formula: .
Dimensions: .
This matches with (iii).
(c) Capacitance (C):
Formula: (since Potential ).
Dimensions of Charge .
Dimensions of Work .
Dimensions of .
This matches with (i).
(d) Planck's constant (h):
Formula: (where is frequency).
Dimensions: .
This matches with (ii).
Step 4: Final Answer:
The correct matching is a-iv, b-iii, c-i, d-ii. This corresponds to code (2).