**Physics**

**Chapter-2**

**Units & Measurements**

*Very Short Answer Type Questions:*

Q1. Is it possible for two quantities to have the same dimensions but different units?

or

If two physical quantities have the same dimension, do they represent same physical content?

Q2. Is it possible for two quantities to have same units but different dimensions?

Q3. Find the SI unit of Pressure.

Q4. What are the dimensions of volume of a cube of edge â€˜aâ€™?

Q5. What are the dimensions of the ratio of the volume of a cube of edge â€˜aâ€™ to the volume of a sphere of radius â€˜aâ€™?

*Short Answer Type Questions:*

Q1. Find the dimensions of (a) linear momentum (b) kinetic energy and (c) frequency.

Q2. Taking force, length and time to be the fundamental quantities find the dimensions of (a) density (b) pressure (c) momentum and (d) energy.

Q3. Suppose the acceleration due to gravity at a certain place is 10 m/s^{2}. Find its value in cm/(minute)^{2}.

Q4. The surface tension of water is 72 dyne/cm. Convert it in SI unit.

Q5. Determine the number of significant figures in the following:

Â Â Â Â Â Â (a) 0.05718 (b) 93.26 (c) 2.35 x 10^{-19} (d) 1.375 x 10^{9}

*Long Answer Type Questions:*

Q1. Derive an expression for the kinetic energy of a body of mass â€˜mâ€™ and moving with velocity â€˜vâ€™, using dimensional analysis.

Q2. An object was weighed by a physical balance and following readings were obtained:

Â Â Â Â Â Â Â 5.04 g ; 5.06 g ; 4.97 g ; 5.00 g ; 4.93 g

Find (i) Mean value (ii) Absolute error (iii) Percentage error

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â [**Ans:** (i) 5.00 g, (ii) 0.04 g, (iii) 0.8 % ]

Q3. The hydrostatic pressure â€˜Pâ€™ of a liquid column depends upon the density â€˜dâ€™, height â€˜hâ€™ of liquid column and also an acceleration â€˜gâ€™ due to gravity. Using dimensional analysis, derive formula for pressure P.Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â [**Ans:** P = k*hdg*]

Q4. Check whether the equations are dimensionally correct or not:

Â Â Â Â Â

Q5. Find the dimensions of Planckâ€™s constant â€˜hâ€™ from the equation Â where E is the energy and Â is the frequency.