Short Question Answers

1. Can we tell the unit of a physical quantity from its dimensions?

Yes, we can tell the unit of a physical quantity. For citation, if a physical quantity has the dimensions [M⁰LT^-2], its SI unit will be ms^-2.

2. Can dimensional analysis tell you that a physical relation is completely right?

Dimensional analysis doesn’t tell us that a physical relation is completely right because that the numerical factors in the relation cannot be determined.

Let v = u + 2at be a physical relation. Dimensional formula of v is [LT^-1] and that of (u+2at) is [LT^-1]. Hence the relation is dimensionally correct but the established fact is that the above relation is not a correct physical relation.

3. Differentiate between accuracy and precision. (VVI)

4. If y = a + bt + ct², where y is the distance and t is the time. What is the dimension and unit of c? (VVI)

Here, y = a + bt + ct²

Applying principle of Homogeneity,”The dimensions of each terms on the two side of correct physical relation must be same.” So, ct² = y ... (i)

Writing eqn (i) in dimensional form,

C [T]² = [L]

C = [L] / [T]²

C = m/s²

Therefore, the unit of C is m/s².

5. Check the correctness of the relation T = 2π √( l/g ) using dimensional analysis. (VVI)

   Dimension of time period (T) = [T]

   Dimension of Length (l) = [L]

   Dimension of gravity (g) = [M⁰LT^-2]

   Dimension of R.H.S [2π √( l/g ) ] = √[L]/ [M⁰LT^-2] = [T]

According to the principle of homogeneity, The dimensions of each term on the two sides of correct physical relation must be same.

Here, in relation T = 2π √( l/g ), the dimension of each term on the two sides is same. So, the given relation is dimensionally correct. 

6. Define: (i) Most probable value (ii) Absolute error (iii) Mean absolute error (iv) Relative error (v)Percentage error (VVI)

1. Most probable value: The mean value, i.e., the arithmetic average of a large number of measurements (assumed to be free from error) of the same quantity is called the most probable value of the quantity.
2. Absolute error: For a set of measurements of the same quantity, the positive difference between each individual value and the most probable value gives the absolute error in the value.
3. Mean absolute error: For a set of measurements of the same quantity, the arithmetic mean of all absolute error gives the mean absolute error in the measurement of that quantity.
4. Relative error:  The ratio of the mean absolute error in the measurement of physical quantity to its most probable value is called relative error in the measurement of that quantity.
5. Percentage error: The relative error in a measurement of a physical quantity multiplied by 100, gives the percentage error of hat measurement.

7. The length of rod is exactly 1cm. An observer records the readings as 1.0cm, 1.00cm and 1.000cm, which is the most accurate measurement?

The measurement 1.000cm is a more accurate measurement because it has a greater number of significant figures. Also, the least count of the device measuring 1.000cm is least of all the other devices i.e. 0.0001cm. As we know larger the significant number greater the accuracy, the third measurement is the accurate measurement.

8. What do you mean by significant figure?

The significant figures of measurement are all those digits which are meaningful i.e. those digits about which we are absolutely sure and a digit which can be doubted. Suppose, a radius of a tennis ball when measured by Vernier calipers is 3.67cm and 3.675 cm when measured by screw gauge, the significant figures are 3 and 4. The more the significant figure more precise is the measurement.

10. What are characteristics of a physical standard?

A physical standard has the following characteristics:

1. Invariability
2. Accessibility
3. Indestructibility
4. Reproducibility

10. Taking force, length and time to be fundamental quantities, find the dimensional formula for density.

Dimension of density (D):

Since, D = mass/Volume

                 = (Force/acceleration)/Volume     [ F = ma, m = F/a]

                 = f/a * V  …………(i)

Dimension of F = [F]

Dimension of acceleration = [LT^-2]

Dimension of volume = [L³]

Equation (i) becomes,

D = [F]/[LT^-2]. [L³]

D = [F L^-4 T²]

The dimensions of D are 1 in F, -4 in L and 2 in T.

Try yourself following Questions;

• Check the correctness of the relation h = 2Tcosθ/ r ρ g, where symbols have their regular meanings.
• A student writes expression if the force causing a body of mass (m) to move in a circular path with velocity v as F = mv². Check the dimensional correctness of the equation.
• Find the dimension of Planck’s constant ‘h’ from the equation: λ = h / p; where λ is wavelength, and p is movement of photon.
• A student writes √R/2 GM for escape velocity. Check the correctness of the formula by using dimensional analysis.
• Determine the dimensional formula for universal Gravitational constant(G).
• Write the dimensional formula for Latent heat, Q = mL where L is latent heat.
• The density of gold is 19.3 gm/cc. Change it into SI unit