Animated Solution for Physics - Physics and Measurement: Match List-I with List-II Choose the correct answer from the options given below.

Welcome to a classic dimensional analysis challenge! This problem is a fantastic opportunity to test your grasp of fundamental physics formulas and how they translate into dimensional representations.

We are presented with a Matrix Match question. On the left side, we have four distinct physical quantities: Planck's constant, kinetic energy, electric potential, and linear momentum. On the right side, we have four dimensional formulas. Our mission is to decode each quantity and find its perfect match.

The key to solving such problems is not to memorize every single dimensional formula, but rather to remember the basic defining equations for each quantity. Let's break them down one by one.

Let's start with Planck's constant ($h$). We know from quantum mechanics that the energy of a photon is directly proportional to its frequency. The equation is:

Rearranging for $h$, we get $h = \frac{E}{ u}$. The dimensional formula for energy ($E$) is $[M{L}^2{T}^{-2}]$, and for frequency ($ u$), it is $[T^{-1}]$. Substituting these in, we find:

This perfectly matches option 2 in the second column.

Next up is Kinetic Energy ($E$). The formula is universally known:

Mass ($m$) has the dimension $[M]$, and velocity ($v$) has $[L{T}^{-1}]$. Squaring the velocity gives $[L^2{T}^{-2}]$. Multiplying by mass, we get:

This matches option 3. Notice how work and all forms of energy share this exact same dimensional formula!

Now, let's tackle Electric Potential ($V$). By definition, electric potential is the work done per unit charge:

We already know work ($W$) has dimensions $[M{L}^2{T}^{-2}]$. Charge ($q$) is current multiplied by time, so its dimension is $[IT]$. Plugging these into our formula:

This corresponds to option 4.

Finally, we have Linear Momentum ($P$). The formula is simply mass times velocity:

Using the fundamental dimensions, we get:

This matches option 1.

With all our derivations complete, we can confidently map the columns.

A $\to$ 2 B $\to$ 3 C $\to$ 4 D $\to$ 1

Dimensional analysis is a powerful tool, not just for matching questions, but for verifying the correctness of complex equations during your exams. Keep practicing these derivations, and they will become second nature!