Physics Chapter on Measurements and Constants

The unit of the expression derived from fundamental physical constants like mass, length, and time, is represented by a combination of the fundamental units, like kg (kilogram) for mass, m (meter) for length, and s (second) for time.

The error in the volume of a sphere is directly proportional to the error in the radius, and since the volume formula involves the radius cubed, the error in volume is three times the error in the radius. Hence, a 2% error in the radius will result in a 6% error in the volume.

The number of significant figures in a measurement indicates the precision of the measurement. The more significant figures, the more precise the measurement.

The dimensional formula of a physical quantity represents the fundamental units (mass, length, time...) that make up the quantity. Planck's constant relates energy to frequency, so its dimensional formula requires units of energy (ML2T-2) and frequency (T-1), resulting in [ML2T-1].

The dimensional formula of a physical quantity represents the fundamental units that make up that quantity. The gravitational constant relates force, mass, and distance, requiring units of force (MLT-2), mass (M), and distance (L) squared. This results in the dimensional formula [M-1L3T-2].

Quantities that can be expressed as a product of fundamental physical quantities like mass, length, and time. They have dimensions and units.

These quantities are derived from fundamental quantities and have their own dimensions and units. Examples include velocity (length/time), acceleration (length/time²), and force (mass * length/time²).

A method for determining the distance to an object by measuring the angle of the object from two different locations, then using trigonometry to calculate the distance. This method requires knowing the distance between the two observation points.

A process of estimating the uncertainty in a measured quantity by analyzing the various sources of error. It is used to determine how the errors in individual measurements propagate to affect the final calculated result.

A method for determining the distance to a distant object by measuring the time it takes for an electromagnetic wave (like radio waves) to travel to that object and back. This method requires knowing the speed of the wave.

A process of determining the significant figures in any measurement by considering its precision and accuracy.

The closeness of repeated measurements of the same quantity to each other; how close measurements are to each other. Example: Measuring the length of a table multiple times and getting very similar values.

The closeness of a measured value to the true or accepted value of a quantity. Example: Measuring the temperature of a room with a thermometer and getting a value close to the actual room temperature.