Unit And Dimensions

Practice Questions:

Question 81: easy

Following observations were taken with a vernier calliper while measuring the length of a cylinder: \(3.29 \text{cm}\), \(3.28 \text{cm}\), \(3.29 \text{cm}\), \(3.31 \text{cm}\), \(3.28 \text{cm}\). The most accurate length of the cylinder will be

1. \(3.28 \text{cm}\)

2. \(3.29 \text{cm}\)

3. \(3.32 \text{cm}\)

4. \(3.21 \text{cm}\)

View Answer

The most accurate value is the mean value of the observations. Mean length = \[\frac{3.29 + 3.28 + 3.29 + 3.31 + 3.28}{5} = \frac{16.45}{5} = 3.29 \text{cm}\].

💬 Discuss this Question

Question 82: easy

Choose the quantities that are dimensionless among the following.

1. \(\frac{\text{Torque}}{\text{Force}}\)

2. \(\frac{\text{Torque}}{\text{Work}}\)

3. \(\frac{\text{Work}}{\text{Energy}}\)

4. Both (2) and (3)

View Answer

Torque, work, and energy all have the same dimensions \([ML^2T^{-2}]\). Hence, \(\frac{\text{Torque}}{\text{Work}}\) and \(\frac{\text{Work}}{\text{Energy}}\) are both dimensionless, while \(\frac{\text{Torque}}{\text{Force}}\) has the dimension of length.

💬 Discuss this Question

Question 83: easy

Two physical quantities \(P\) and \(Q\) have different dimensions. The mathematical operation that is not possible among the following are

1. \(\frac{P}{Q}\)

2. \(PQ\)

3. \(P + Q\)

4. Both (1) and (2)

View Answer

According to the principle of homogeneity of dimensions, only quantities with identical dimensions can be added or subtracted. Multiplication and division of different physical quantities are allowed.

💬 Discuss this Question

Question 84: easy

In an experiment, the percentage error occurring in the measurements of physical quantities \( A \), \( B \) and \( C \) are 1%, 2% and 3% respectively. If a physical quantity \( X \) is such that \( X = \frac{AB^2}{C^3} \), then the percentage error in the calculation of \( X \) can be

1. 1%

2. 2%

3. 3%

4. 4%

View Answer

By taking systematic errors into account, the relative error can be written with signs: \( \frac{\Delta X}{X} = \pm \frac{\Delta A}{A} \pm 2\frac{\Delta B}{B} \pm 3\frac{\Delta C}{C} \). The minimum absolute error is \( |1 + 4 - 9|\% = 4\% \), so 4% is a possible value.

💬 Discuss this Question

Question 85: easy

Sum of the numbers \(436.32\text{ g}\), \(227.2\text{ g}\) and \(0.301\text{ g}\) is

1. 663.821 g

2. 663.8 g

3. 6663.82 g

4. 664 g

View Answer

In addition, the final result must be rounded off to the least number of decimal places of the terms. Here, \(227.2\text{ g}\) has one decimal place, so the sum \(663.821\text{ g}\) is rounded to \(663.8\text{ g}\).

💬 Discuss this Question

« Previous 1 … 7 8 9