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Questions and Answers
How far is the nearest star to our solar system in terms of light-years?
How far is the nearest star to our solar system in terms of light-years?
What is the approximate distance of the nearest star to our solar system in parsecs?
What is the approximate distance of the nearest star to our solar system in parsecs?
What is the unit of self-inductance of a coil?
What is the unit of self-inductance of a coil?
Which is the correct unit of stress?
Which is the correct unit of stress?
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If each main scale division is 0.5 mm, what is the minimum inaccuracy in the measurement of distance?
If each main scale division is 0.5 mm, what is the minimum inaccuracy in the measurement of distance?
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What is the speed of sound in water?
What is the speed of sound in water?
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What are the units of $K = rac{1}{4 ext{π} ext{ε}_0}$?
What are the units of $K = rac{1}{4 ext{π} ext{ε}_0}$?
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What is the area of a sheet with length 10.2 cm and width 6.8 cm, expressed with proper significant figures?
What is the area of a sheet with length 10.2 cm and width 6.8 cm, expressed with proper significant figures?
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How much is 1 degree angle in radians?
How much is 1 degree angle in radians?
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What is the assertion about linear mass density?
What is the assertion about linear mass density?
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What is the dimension of k in the wave equation Y = A sin(ωx - kt)?
What is the dimension of k in the wave equation Y = A sin(ωx - kt)?
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In which system of units is Weber the unit of magnetic flux?
In which system of units is Weber the unit of magnetic flux?
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How many significant figures are there in the measured value 0.0204?
How many significant figures are there in the measured value 0.0204?
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What is the dimension of the viscous damping constant proportional to the velocity of an object in a liquid?
What is the dimension of the viscous damping constant proportional to the velocity of an object in a liquid?
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Which equation correctly represents the kinetic energy of an object?
Which equation correctly represents the kinetic energy of an object?
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What does the constant in the damping force equation depend on?
What does the constant in the damping force equation depend on?
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In the context of wave motion, what does ω represent?
In the context of wave motion, what does ω represent?
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Which of the following is NOT a factor in determining potential energy?
Which of the following is NOT a factor in determining potential energy?
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What is the distance of the tower C from the original position A if the parallax angle is θ = 40°?
What is the distance of the tower C from the original position A if the parallax angle is θ = 40°?
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Which of the following pairs of quantities have the same dimensions?
Which of the following pairs of quantities have the same dimensions?
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In ensuring maximum accuracy for measuring the physical quantity X, which measurable should be measured most precisely?
In ensuring maximum accuracy for measuring the physical quantity X, which measurable should be measured most precisely?
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What is the percentage error in the measured quantity X if the percentage errors in a, b, c, and d are 1%, 2%, 3%, and 4% respectively?
What is the percentage error in the measured quantity X if the percentage errors in a, b, c, and d are 1%, 2%, 3%, and 4% respectively?
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What is the formula for the physical quantity X if it depends on four measurables a, b, c, and d?
What is the formula for the physical quantity X if it depends on four measurables a, b, c, and d?
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How long is the time delay measured by a SONAR system based on the information provided?
How long is the time delay measured by a SONAR system based on the information provided?
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Which physical principle does SONAR utilize to detect underwater objects?
Which physical principle does SONAR utilize to detect underwater objects?
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What would be the primary concern when determining the accuracy of a physical quantity like X?
What would be the primary concern when determining the accuracy of a physical quantity like X?
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What is the dimensional formula for energy when momentum, area, and time are considered as fundamental quantities?
What is the dimensional formula for energy when momentum, area, and time are considered as fundamental quantities?
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What is the density of the Sun given its mass and radius?
What is the density of the Sun given its mass and radius?
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How many pico Farads is equivalent to one Farad?
How many pico Farads is equivalent to one Farad?
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What is the maximum time difference expected between two caesium clocks running for 100 years?
What is the maximum time difference expected between two caesium clocks running for 100 years?
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If momentum, area, and time are fundamental quantities, which expression represents the fractional error in calculating z?
If momentum, area, and time are fundamental quantities, which expression represents the fractional error in calculating z?
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What unit is identified as the unit of power?
What unit is identified as the unit of power?
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What is the angular diameter of Jupiter when viewed from a distance of 824.7 million kilometers?
What is the angular diameter of Jupiter when viewed from a distance of 824.7 million kilometers?
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How varies the expected time difference between two caesium clocks over a 100 year duration?
How varies the expected time difference between two caesium clocks over a 100 year duration?
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What is the proper conversion of one pico Farad into scientific notation?
What is the proper conversion of one pico Farad into scientific notation?
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What is the significance of the state of two caesium clocks differing by 0.02 sec over a century?
What is the significance of the state of two caesium clocks differing by 0.02 sec over a century?
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Study Notes
Dimensional Analysis
- Dimensional Formula - A formula that expresses the relationship between a physical quantity and fundamental quantities (like mass, length, and time).
- Fundamental Quantities - Basic quantities that cannot be expressed in terms of other physical quantities, like mass, length, and time.
- Derived Quantities - Quantities expressed in terms of fundamental quantities, like velocity, force, and energy.
Dimensional Formula for Energy
- Assuming momentum (p), area (A), and time (T) are fundamental quantities, the dimensional formula for energy is [pA−1T1].
Density of the Sun
- The density of the Sun is 1.4 x 103 kg m-3.
- It is calculated using the mass of the Sun (2.0 x 1030 kg) and its radius (7.0 x 108 m).
Standard Caesium Clock Accuracy
- Two Caesium clocks running for 100 years may differ by only 0.02 seconds.
- This implies that the accuracy of the standard Caesium clock in measuring a time interval of 1 second is 1011 to 1012.
Fractional Error
- If z = (A x B) / (A + B), the fractional error in z is given by [(△A / A) + (△B / B)] / (A + B), where △A and △B are the errors in determining A and B.
Unit of Power
- The unit of power is Joule per second (J/s) and watt (W).
Minimum Inaccuracy of Measurement
- The minimum inaccuracy in the measurement of distance using a main scale division of 0.5 mm is 0.01 mm.
Nearest Star to our Solar System
- The nearest star to our solar system is 4.29 light-years away.
- This distance is equivalent to 1.32 parsecs.
Parallax
- Parallax is the angle between the line of sight to an object and the line of sight to the same object from a different location.
- It can be used to measure distances to nearby stars.
Unit of Self Inductance
- The unit of self-inductance of a coil is Henry (H).
Unit of Stress
- The unit of stress is Newton per square meter (N/m2).
Quantities with Same Dimensions
- The pair of quantities having the same dimensions is wavelength and focal length.
Maximum Accuracy in Determining X
- Given X = (a2b) / (c5d), to ensure the maximum accuracy in determining X, the quantity c should be measured with maximum accuracy.
Percentage Error in Quantity X
- If X = (a2b3c5/2) / d-2, the percentage error in X is 34.6 %.
Units of K
- Given K = 1 / (4πε0), the units of K are Nm2C−2.
Area Calculation with Significant Figures
- The area of a sheet with length 10.2 cm and width 6.8 cm, addressed to the proper number of significant figures is 69 cm2.
Degree to Radian Conversion
- 1 degree (°)= 1.745 x 10-2 radian.
Dimensional Formula of k
- Given the wave equation Y = A sin(ωt - kx), the dimension of k is T−1.
Weber as Unit of Magnetic Flux
- The unit Weber (Wb) is used to measure magnetic flux in the SI system.
Dimension of Constant of Proportionality (Viscous Damping)
- The viscous damping force is proportional to velocity.
- The dimension of the proportionality constant is M0LT−1.
Significant Figures in Measured Value
- The number of significant figures in the measured value 0.0204 is three.
Dimensions of Potential Energy
- The dimensions of potential energy are ML2T−2.
Muscle Times Speed Equals Power
- The athletic coach's statement "muscle times speed equals power" is incorrect.
- Power is actually calculated as force multiplied by velocity.
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Description
Test your knowledge on dimensional analysis, including fundamental and derived quantities, as well as the dimensional formula for energy. This quiz will also cover practical applications, like the density of the Sun and the accuracy of Caesium clocks.
