Physics MCQs Explained: Travelling Microscope & Dipole Moments
Let’s solve two conceptual physics questions — one from experimental optics (Least Count) and another from electromagnetic dimensions (Dipole Moments). Both test your analytical approach and formula application.
Question 1: Least Count of a Travelling Microscope
Problem: For the determination of the refractive index of a glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equal to 15 cm. The vernier scale attached to the microscope has 25 divisions equal to 24 divisions of the main scale. Find the least count (LC) of the travelling microscope in cm.
Solution:
\( 300\ \text{MSD} = 15\ \text{cm} \Rightarrow 1\ \text{MSD} = 0.05\ \text{cm} \)
\( 25\ \text{VSD} = 24\ \text{MSD} \Rightarrow 1\ \text{VSD} = \frac{24}{25}\ \text{MSD} \)
\( \text{LC} = 1\ \text{MSD} - 1\ \text{VSD} = \frac{1}{25}\ \text{MSD} = 0.002\ \text{cm} \)
✅ Least Count of Travelling Microscope = 0.002 cm
Question 2: Dimensional Analysis of Dipole Moments
Problem: In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has the dimension \( [M^P L^Q T^R A^S] \). Find P and Q.
Electric dipole moment: \( \vec{P} = q \times 2\ell \)
Magnetic dipole moment: \( \vec{M} = I A \)
Dimensions:
\( [P] = [L T A] \), \( [M] = [L^2 A] \)
\( \frac{[P]}{[M]} = [L^{-1} T] = M^0 L^{-1} T^1 A^0 \)
Hence, \( P = 0, Q = -1 \).
✅ Correct Answer: P = 0, Q = −1
Summary
- Least Count: 0.002 cm
- Dimensional Ratio: \( L^{-1}T^1 \), where P = 0, Q = −1
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