H C Verma solutions, Introduction to Physics, Objective-II, Chapter-1, Concepts of Physics, Part-I Introduction to Physics

HC Verma Solutions – Concepts of Physics Part 1

Chapter 1: Introduction to Physics – Objective II

Q1. The dimensions ML⁻¹T⁻² may correspond to:

• (a) work done by a force
• (b) linear momentum
• (c) pressure
• (d) energy per unit volume

Answer: (c), (d)

Solution:

• Work done/energy = Force × distance = [MLT⁻²][L] = [ML²T⁻²] → does not match.
• Linear momentum = mass × velocity = [M][LT⁻¹] = [MLT⁻¹] → does not match.
• Pressure = Force / Area = [MLT⁻²] / [L²] = [ML⁻¹T⁻²] → correct.
• Energy per unit volume = [ML²T⁻²] / [L³] = [ML⁻¹T⁻²] → correct.

Q2. Choose the correct statement(s):

• (a) A dimensionally correct equation may be correct.
• (b) A dimensionally correct equation may be incorrect.
• (c) A dimensionally incorrect equation may be correct.
• (d) A dimensionally incorrect equation may be incorrect.

Answer: (a), (b), (d)

Solution: A dimensionally correct equation may or may not be physically correct (examples exist for both). Hence (a) and (b) are valid. A correct equation must also satisfy dimensional correctness, so a dimensionally incorrect equation cannot be correct → (c) is false, (d) is true.

Q3. Choose the correct statements:

• (a) All quantities may be represented dimensionally in terms of the base quantities.
• (b) A base quantity cannot be represented dimensionally in terms of the rest of the base quantities.
• (c) The dimension of a base quantity in other base quantities is always zero.
• (d) The dimension of a derived quantity is never zero in any base quantity.

Answer: (a), (b), (c)

Solution:

• All physical quantities (derived quantities) can be expressed in terms of base quantities → (a) is correct.
• Each base quantity is independent, so it cannot be expressed using the other base quantities → (b) is correct.
• That’s why the dimension of one base quantity in terms of another is always zero → (c) is correct.
• Some derived quantities may have zero dimensions in certain base quantities (e.g., velocity has zero dimension in mass, frequency has zero dimension in both mass and length) → so (d) is incorrect.