Units and Measurements

In the CGS (centimeter-gram-second) system, the unit of force is the dyne. One dyne is the force required to accelerate a mass of one gram at a rate of one centimeter per second squared. Newton is the SI unit of force, erg is a unit of energy in CGS, and joule is the SI unit of energy.

The least count of a Vernier caliper is calculated as the difference between one main scale division (MSD) and one Vernier scale division (VSD). Typically, 10 Vernier scale divisions coincide with 9 main scale divisions. If one main scale division is 1 mm, then one Vernier scale division is 0.9 mm. Therefore, the least count = 1 mm - 0.9 mm = 0.1 mm. Hence, the correct least count is 0.1 mm, which corresponds to option C.

The CGS system (centimeter-gram-second) is a variant of the metric system and is also known as the Metric or French system of units, as it originated in France and is based on metric units.

Velocity is defined as displacement per unit time. Displacement has the dimension of length (L), and time has the dimension (T). Therefore, the dimension of velocity is length divided by time, which is LT^-1.

A radian is a unit of angular measure, not length. Light year, angstrom, and micron are all units used to measure length or distance.

Speed is a scalar quantity because it has only magnitude and no direction, unlike displacement, velocity, and acceleration which are vector quantities having both magnitude and direction.

The SI unit of acceleration is meters per second squared (m/s²), which represents the change in velocity per unit time. Option B correctly states this unit.

The international prototype kilogram, historically kept near Paris, is a platinum-iridium cylinder with a mass of exactly 1 kilogram. This standard was used to define the kilogram until the redefinition based on physical constants.

In the CGS (centimeter-gram-second) system, the unit of force is the dyne, defined as the force required to accelerate a mass of one gram at a rate of one centimeter per second squared. Newton and pound are units from other systems (SI and Imperial respectively).

Power is defined as the rate of doing work or the rate of energy transfer, and its SI unit is the watt (W). Joule is a unit of energy, Newton is a unit of force, and Pascal is a unit of pressure.

Length, mass, time, intensity of light, and amount of substance are fundamental physical quantities that are defined independently and serve as the basis for other measurements; hence, they are called base quantities.

1 atmosphere (atm) is defined as exactly 760 torr, which is equivalent to 760 mmHg, and also approximately equal to 101.3 kilopascals (kPa). Therefore, all the given options are correct.

To convert speed from mph to m/s, multiply by 0.44704. Thus, 100 mph × 0.44704 ≈ 44.7 m/s, which rounds to 45 m/s, making option A correct.

The SI unit of time is the second, which is the standard unit used worldwide for measuring time intervals.

The SI base unit for mass is the kilogram (kg), which is the internationally accepted standard unit for measuring mass. Other options like gram, pound, and ounce are units of mass but are not the SI base unit.

The current SI standard for the unit of time, the second, is defined based on the frequency of radiation emitted by the transition between two hyperfine levels of the ground state of the cesium-133 atom. Specifically, one second is defined as the duration of 9,192,631,770 periods of this radiation. Historically, krypton-86 was used for defining the meter, not the second. Therefore, among the given options, the closest and correct answer is B, although it should refer to cesium-133 rather than krypton-86. The other options (daily rotation of the earth, yearly revolution of the earth, and precision pendulum clock) are not the basis for the current SI definition of the second.

The SI base unit for mass is the kilogram (kg), which is the internationally accepted standard unit for measuring mass. Other options like gram, pound, and ounce are not SI base units.

The SI unit of time, the second, is defined based on the frequency of radiation emitted by the transition between two hyperfine levels of the ground state of the cesium-133 atom, but historically it was defined using the frequency of light emitted by krypton-86. Among the given options, the frequency of light emitted by Kr86 is the closest and historically relevant definition.

The candela is the SI base unit of luminous intensity, which measures the perceived power of light emitted in a particular direction. It is not related to heat, temperature, or radioactive decay.

A steradian is the SI unit used to measure solid angles, analogous to how radians measure plane angles. It quantifies the two-dimensional angle in three-dimensional space.

One British Thermal Unit (BTU) is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit, which is approximately equal to 1055 joules. This makes option C the correct answer.

One Joule is equal to 10^7 ergs because 1 erg is 10^-7 Joules, so converting Joules to ergs involves multiplying by 10^7.

One gram weight exerts a force due to gravity approximately equal to 981 dynes, since 1 dyne is the force required to accelerate 1 gram at 1 cm/s² and standard gravity is about 980 cm/s².

One British Thermal Unit (BTU) is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit, which is approximately equal to 2055 Joules.

One Torr is defined as exactly 1 millimeter of mercury (mmHg). This unit is commonly used to measure pressure and is equivalent to the pressure exerted by a 1 mm column of mercury.