Q1: The standard unit of time in the International System of Units (SI) is ____________.
Ans: Second (s)
Q2: The diameter of a circle is a ___________ quantity.
Ans: Scalar
Q3: The Vernier scale is used for measuring ________.
Ans: Length
Q4: The dimensions of the coefficient of viscosity (η) are _________.
Ans: ML^{1}T^{1}
Q5: The precision of a measurement is determined by the number of ____________.
Ans: Significant Figures
Ans:
Q1: Which of the following is a base unit in the International System of Units (SI)?
(a) Newton
(b) Kilogram
(c) Joule
(d) Pascal
Ans: (b) Kilogram
Q2: The least count of a Vernier caliper is 0.01 cm. If the main scale reading is 2.3 cm and the Vernier scale reading is 0.08 cm, the correct measurement is:
(a) 2.31 cm
(b) 2.32 cm
(c) 2.38 cm
(d) 2.4 cm
Ans: (a) 2.31 cm
Q3: The dimension of speed is:
(a) [M^{0}L^{1}T^{1}]
(b) [M^{0}L^{0}T^{1}]
(c) [M^{1}L^{0}T^{1}]
(d) [M^{1}L^{1}T^{1}]
Ans: (c) [M^{1}L^{0}T^{1}]
Q4: Which of the following is not a derived unit?
(a) Newton (N)
(b) Meter (m)
(c) Watt (W)
(d) Pascal (Pa)
Ans: (b) Meter (m)
Q5: A car travels a distance of 400 meters in 20 seconds. What is its average speed?
(a) 20 m/s
(b) 40 m/s
(c) 5 m/s
(d) 2 m/s
Ans: (a) 20 m/s
Q1: Assertion: The dimensions of angular velocity are [M^{0}L^{0}T^{1}].
Reason: Angular velocity is a scalar quantity.
Ans: False
The dimensions of angular velocity are [M^{0}L^{0}T^{2}], and angular velocity is a vector quantity.
Q2: Assertion: Two physical quantities having the same dimensions are always equal. Reason: Dimensions are just labels and do not affect the numerical value of a quantity.
Ans: False
Two physical quantities having the same dimensions may not be equal; numerical values and units matter.
Case 1: A student measures the length of a pencil using two different rulers. Ruler A has a least count of 0.1 cm, and ruler B has a least count of 0.01 cm. The student obtains measurements of 7.2 cm using ruler A and 7.25 cm using ruler B. Calculate the percentage error in each measurement and discuss the precision of each ruler.
Solution: Measurement with Ruler A: Measured length = 7.2 cm Least count = 0.1 cm Percentage error = [(0.1 cm) / (7.2 cm)] × 100% = 1.39%
Measurement with Ruler B: Measured length = 7.25 cm Least count = 0.01 cm Percentage error = [(0.01 cm) / (7.25 cm)] × 100% = 0.14%
Ruler A has a higher percentage error, indicating lower precision compared to Ruler B.
Case 2: A student measures the time taken for a pendulum to complete 10 oscillations. He records three sets of measurements as follows: 14.5 s, 14.3 s, and 14.4 s. Calculate the mean time and the absolute error in the measurement.
Solution: Mean time = (14.5 s + 14.3 s + 14.4 s) / 3 = 14.4 s Absolute error = 14.4 s  14.5 s = 0.1 s
The mean time is 14.4 seconds, and the absolute error is 0.1 seconds.
Q1: Define dimensional analysis. How is it useful in physics? (Word Limit: 100120 words)
Ans: Dimensional analysis is a mathematical technique used in physics to analyze and understand the relationships between physical quantities. It involves examining the dimensions (fundamental units like mass, length, time, etc.) of various physical quantities and how they combine in equations. Dimensional analysis is useful in physics for the following reasons:
Q2: Explain the difference between precision and accuracy in measurements. (Word Limit: 100120 words)
Ans: Precision and accuracy are two important aspects of measurements that describe different characteristics:
Q3: Differentiate between scalar and vector quantities with examples. (Word Limit: 100120 words)
Ans: Scalar and vector quantities are types of physical quantities with distinct characteristics:
Q4: State and explain the principle of the Vernier caliper. (Word Limit: 100120 words)
Ans: The Vernier caliper is a precision instrument used for measuring the length of an object with high accuracy. Its principle is based on the Vernier scale, which consists of a main scale (fixed) and a Vernier scale (sliding).
The principle of the Vernier caliper is as follows:
Q5: Explain the concept of relative error in measurements. (Word Limit: 100120 words)
Ans: Relative error is a measure of the accuracy of a measurement and is expressed as the ratio of the absolute error to the true value of the quantity being measured. It is often represented as a percentage. The formula for relative error is: Relative Error (%) = [(Absolute Error) / (True Value)] × 100%
Key points about relative error:
Q1: Discuss the importance of units and measurements in scientific research. (Word Limit: 150200 words)
Ans: Units and measurements play a crucial role in scientific research for several reasons:
Q2: Explain the principle of the Vernier scale in detail and provide a stepbystep procedure for using a Vernier caliper to measure the length of an object. (Word Limit: 150200 words)
Ans: The Vernier caliper is a precision instrument used to measure the length, diameter, or thickness of objects with great accuracy. Its principle is based on the Vernier scale, which allows for precise readings.
Principle of the Vernier Scale:
Procedure for Using a Vernier Caliper:
The accuracy of a Vernier caliper is typically up to 0.02 mm or 0.001 inches, making it suitable for precise measurements.
Q3: Explain the concept of significant figures in measurements. Provide examples of how to determine the number of significant figures in various measurements. (Word Limit: 150200 words)
Ans: Significant figures (sig figs) are digits in a measurement that convey meaningful information about the precision and accuracy of that measurement. They are important for representing the uncertainty associated with a measurement. Here's how to determine the number of significant figures in various measurements:
Nonzero digits are always significant. For example:
Any zeros between significant figures are also significant. For example:
Leading zeros (zeros to the left of the first nonzero digit) are not significant. For example:
Trailing zeros (zeros to the right of nonzero digits and after the decimal point) are significant. For example:
In whole numbers without a decimal point, trailing zeros may not be considered significant. For example:
In scientific notation, all digits in the coefficient are significant. For example:
In calculations involving measurements, the result should be rounded to the least number of significant figures in the original data to maintain accuracy and avoid false precision.
Q4: Discuss the process of dimensional analysis with an example. (Word Limit: 150200 words)
Ans: Dimensional analysis is a powerful technique used in physics to derive relationships between physical quantities and verify equations. It is based on the principle that physical equations must be dimensionally consistent. Here's a stepbystep process of dimensional analysis with an example:
Example: Derive an equation for the period (T) of a simple pendulum using dimensional analysis.
Step 1: List the Relevant Variables
Step 2: Write the Basic Equation
T = k * L^{m} * g^{n}
Step 3: Assign Dimensions
Step 4: Equate Dimensions
Step 5: Solve for Exponents
Step 6: Final Equation
The final equation for the period of a simple pendulum is T = k * (L / g), where k is a dimensionless constant.
Q5: Explain the concept of the International System of Units (SI) and its importance in scientific measurements. Provide examples of SI units for various physical quantities. (Word Limit: 150200 words)
Ans: The International System of Units (SI) is a globally accepted system of measurement used in scientific research and everyday life. It is based on seven fundamental SI base units, and all other units are derived from these base units. The importance of SI units in scientific measurements is paramount due to the following reasons:
Standardization: SI provides a standardized and consistent system of units, ensuring that measurements made by scientists worldwide are easily understood and compared.
Precision: SI units are designed to be precise and based on physical constants, making them suitable for highly accurate measurements.
Interchangeability: SI units allow easy conversion between units, facilitating communication and calculations in scientific research.
Examples of SI base units:
Examples of SI derived units:
In summary, SI units provide a standardized, precise, and internationally recognized system of measurement essential for scientific research and technological advancements.
Q1: Find the dimensions of (a/b) in the equation: where P is pressure, x is distance and t is time.
Ans:
Q2: Find an expression for viscous force F acting on a tiny steel ball of radius r moving in a viscous liquid of viscosity η with a constant speed ν by the method of dimensional analysis.
Ans: It is given that viscous force F depends on (i) the radius r of steel ball, (ii) the Speed v of the tiny steel ball, and (iii) the coefficient of viscosity η of viscous liquid.
Wriring dimensional formula for given quantities, we have
According to given condition we can write
Comparing powers of M, L and T on either side of equation, we get
c = 1
a + b  c = 1
 b  c = 2
On solving, these above equations, we get
a = 1, b = 1 and c = 1
Hence, the relation becomes
f = krηv
Here, k is constant of proportionality
Q3: Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?
Ans:
Let the period of revolution of the earth = T_{e}
As the planet goes round the sun twice as fast as the earth, so its period of revolution is
Orbital size of the earth, ac = 1 AU
Orbital size of the planet, ap = ?
From Kepler's law of periods,
Q4: A great physicist of this century (P.A.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (c, e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (15 billion years). From the table of fundamental constants in the book, try to see if you too can construct this number (or any other interesting number you can think of). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants?
Ans:
Paul Dirac was a British theoretical physicist who made fundamental contributions to the development of quantum mechanics, quantum field theory and quantum electrodynamics and is particularly known for his attempts to unify the theories of quantum mechanics and relativity theory.
One relation consists of some fundamental constants that give the age of the Universe by:
Where, t = Age of Universe, e = Charge of electrons = 1.6 x 10^{19}C
ε_{0} = Absolute permittivity, mp = Mass of protons = 1.67 x 10^{27} kg
m_{e} = Mass of electrons = 9.1 x 10^{31} kg c = Speed of light = 3 x 10^{8} m/s
G = Universal gravitational constant = 6.67 x 10^{11} Nm2 Kg^{2}
Also,
Substituting these values in the equation, we get
= 6 billion years (which is the approximate age of our universe)
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1. What are the basic units of measurement? 
2. How do you convert between different units of measurement? 
3. Why is it important to use standard units of measurement? 
4. What are the prefixes used in the metric system? 
5. How do you measure the volume of irregularly shaped objects? 

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