Dimensional Analysis and Units

The video tutorial covers solving problems from HC Verma's book, focusing on Young's modulus conversion, dimensional analysis for mass using velocity, time, and force, and checking dimensional consistency in an equation of motion. The instructor explains the conversion of units from Newton per meter square to dyne per centimeter square, derives the dimensional formula for mass, and verifies the dimensional consistency of a motion equation.

What is the unit of Young's Modulus in the CGS system?

• Joule

• Pascal

• Dyne per centimeter square

• Newton per meter square

How many dynes are equivalent to one Newton?

• 10^6

• 10^5

• 10^4

• 10^3

In the conversion of Young's Modulus, what is the equivalent of 1 meter in centimeters?

• 1000 cm

• 10,000 cm

• 100 cm

• 10 cm

Which of the following is NOT a fundamental unit in the context of Problem 5?

• Mass

• Time

• Velocity

• Force

How is mass expressed in terms of force, time, and velocity?

• Velocity multiplied by time divided by force

• Force multiplied by time divided by velocity

• Force multiplied by velocity divided by time

• Time multiplied by force divided by velocity

What is the dimensional formula for mass in terms of force, time, and velocity?

• F T V

• F V T^-1

• F T V^-1

• F^-1 T V

Which equation of motion is being analyzed dimensionally in Problem 6?

• v = u + at

• s = vt - 1/2 at^2

• v^2 = u^2 + 2as

• s = ut + 1/2 at^2

What is the dimensional formula for velocity?

• L T^-1

• L T^2

• M L T^-2

• M L^2 T^-1

In the dimensional analysis of the equation of motion, what is the dimension of acceleration?

• M L T^-2

• M L^2 T^-1

• L T^-2

• L T^-1

What must be true for an equation to be dimensionally correct?

• The variables on both sides must be the same

• The units on both sides must be the same

• The dimensions on both sides must be the same

• The numerical values on both sides must be the same