Questions on Dimension Analysis

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Instructor: Saurabh Verma

Mob: +91 9956551609

Q.1: Define the term 'Dimension'. Give the example of three dimensionless quantities.

Q.2: Define the 'principle of homogeneity of dimensions'.

Q.3: List all the fundamental quantities and their units.

Q.4: What are uses of dimensional analysis? What are limitation of dimension analysis?

Q.5: A book with many printing errors contains four different formulas for the displacement 'y' of a particle undergoing a certain periodic motion:

1. y = a sin (2πt/T)
2. y = a sin (vt)
3.  y = (a/T) sin (t/a)
4.  y = (a/2) (sin (2πt/T) + cos(2πt/T) )

Where a: maximum displacement of the particle, v: speed of the particle and T= time period of motion. Rule out the wrong formulas on dimensional ground.

Q.6: If dimension of A and B are different, which of the followings is possible?

1. A+B
2. A-B
3. A/B
4. A/e^AB

Q.7: Compute the dimension of the followings:

1. Voltage
2. Resistance
3. Pressure
4. Gas constant

Q.8: Convert followings using method of dimensions.

1. 10 dyne into Newton.
2. One erg into joules.

Q.9: A student while doing an experiment finds that the velocity of an object varies with time and it can be expressed as equation:

v = Xt² + Y/(A+g) + Z

if units of v, t and g expressed in SI units, determine the unit of constants X, Y, A and Z.

Q.10: If Force (F), Velocity (V) and Acceleration (A) are taken as the fundamental units instead of mass, length and time, express Pressure and impulse in terms of given fundamental units.

Q.11: Which of the following pairs has the same dimensions?

1. Specific heat and latent heat
2. Impulse and momentum
3. Surface tension and force
4. Moment of inertia and torque

Q.12: In Formula tan (mx/ac) = be^ct, m is mass, x is displacement and t is time. Find out the dimension of a, b and c.

Q.13: The speed of sound v in a gas depends on the pressure p, the density r and the volume V of the gas. Find out the appropriate formula for speed of sound.

"Practice makes a man perfect"