Units And Measurement

Concept: Average speed is calculated as the total distance traveled divided by the total time taken. Average Speed = . We need to ensure units are consistent, and the final answer is required in m/s. Step 1: Identify given distance and time Distance ( ) = 100 km Time ( ) = 2 hours Step 2: Calculate average speed in km/hr Average Speed (km/hr) = . Step 3: Convert km/hr to m/s To convert km/hr to m/s, we use the following conversions: 1 km = 1000 meters (m) 1 hour = 3600 seconds (s) (since 1 hour = 60 minutes, and 1 minute = 60 seconds) So, . Therefore, to convert km/hr to m/s, multiply by . Average Speed (m/s) = Step 4: Calculate the numerical value Now, perform the division: . So, Average Speed (rounded to two decimal places). This matches option (3).

Concept: The SI unit of the universal gravitational constant (G) can be derived from Newton's Law of Universal Gravitation. Newton's Law of Universal Gravitation states: , where:
is the gravitational force between two masses.
is the universal gravitational constant.
and are the two masses.
is the distance between the centers of the two masses. Step 1: Rearrange the formula to solve for G Step 2: Identify the SI units for each quantity in the formula
Force ( ): Newton (N)
Distance ( ): meter (m)
Mass ( , ): kilogram (kg) Step 3: Substitute the SI units into the rearranged formula for G Unit of G = Unit of G = Unit of G = Step 4: Express the unit using negative exponents This can also be written as: Unit of G = This matches option (4).

Concept: The Newton (N) is the SI unit of force. The Dyne is the CGS (Centimeter-Gram-Second) unit of force. We need to find the conversion factor between them. Force is defined by Newton's second law: (Force = mass acceleration). Step 1: Define 1 Newton in terms of base SI units In the SI system:
Mass ( ) is measured in kilograms (kg).
Acceleration ( ) is measured in meters per second squared ( ). So, . Step 2: Define 1 Dyne in terms of base CGS units In the CGS system:
Mass ( ) is measured in grams (g).
Acceleration ( ) is measured in centimeters per second squared ( ). So, . Step 3: Convert kilograms to grams and meters to centimeters We know:

Step 4: Express 1 Newton in CGS units Substitute the conversions from Step 3 into the definition of 1 Newton from Step 1: Since , we have: Therefore, 1 Newton is equal to Dynes. This matches option (1).

Concept: Different physical quantities have specific units. The oersted (Oe) is a unit associated with magnetism. Step 1: Identifying the Oersted unit The oersted is a unit used in the CGS (centimeter-gram-second) system of units. It is named after Hans Christian Ørsted, who discovered the relationship between electricity and magnetism. Step 2: What quantity does the Oersted measure? The oersted is a unit of magnetic field strength, specifically the magnetizing field strength, often denoted by . In the CGS system, magnetic field strength is measured in oersteds. The magnetic flux density (another way to describe a magnetic field) is measured in gauss (G) in the CGS system. These are related by , where is the permeability of the medium. In vacuum, in the CGS EMU system, so (in gauss) and (in oersteds) are numerically equal in vacuum, though they represent distinct physical concepts. Step 3: SI unit for magnetic field strength In the SI system (International System of Units), the unit for magnetic field strength is amperes per meter (A/m). The SI unit for magnetic flux density is the tesla (T). . . Step 4: Analyzing the options
(1) Magnetic field: Correct. Oersted is a unit of magnetic field strength ( ).
(2) Electrical current: The SI unit is ampere (A).
(3) Electrical field: The SI unit is volts per meter (V/m) or newtons per coulomb (N/C).
(4) Magnetic current: This is not a standard physical quantity in the same way as electric current. The concept of magnetic monopole current is theoretical. Therefore, oersted is a unit of magnetic field.

Concept: Each fundamental physical quantity has a standard unit in the International System of Units (SI). Step 1: Define Electrical Current Electrical current (symbol: ) is the rate of flow of electric charge. If a charge flows past a point in a time , the current is . Step 2: Identify the SI unit of Electrical Current The SI unit for electrical current is the ampere (symbol: A). One ampere is defined as one coulomb of charge flowing per second (1 A = 1 C/s). Step 3: Units of other options
Coulomb (C): The SI unit of electric charge ( ).
Joule (J): The SI unit of energy or work ( or ).
Volt (V): The SI unit of electric potential difference or voltage ( ). (1 V = 1 J/C). Therefore, the unit of electrical current is the ampere.

Concept: The power of a lens is a measure of its ability to converge or diverge light. It is defined as the reciprocal of its focal length. Step 1: Define the power of a lens The power ( ) of a lens is given by the formula: where is the focal length of the lens. Step 2: SI unit of focal length The focal length ( ) is a distance. The SI unit of distance is the meter (m). For the power of a lens to be expressed in its standard unit (Diopter), the focal length must be expressed in meters. Step 3: Determine the SI unit of power If is in meters (m), then the unit of power would be (reciprocal meter or per meter). This unit, , is specifically named the Diopter (D). So, . Step 4: Evaluate the given options
(1) Diopter: This is the correct SI unit for the power of a lens.
(2) Decibel (dB): This is a logarithmic unit used to express ratios, commonly for sound level or signal power in electronics. It is not the unit for the power of a lens.
(3) Meter (m): This is the SI unit of length (and focal length), not power of a lens.
(4) Gauss (G): This is a unit of magnetic flux density (magnetic field strength) in the CGS system. It is not related to the power of a lens. Therefore, the S.I. unit of power of lens is Diopter.

Concept: Weight is a type of force. Specifically, it is the gravitational force exerted on an object by a celestial body (like Earth, Moon, etc.). Step 1: Define weight Weight ( ) of an object is given by the product of its mass ( ) and the acceleration due to gravity ( ) at its location: Step 2: Determine the SI units of mass and acceleration due to gravity
The SI unit of mass ( ) is the kilogram (Kg).
The SI unit of acceleration ( , or any acceleration) is meters per second squared ( or ). Step 3: Determine the SI unit of force According to Newton's Second Law of Motion, force ( ) is equal to mass ( ) times acceleration ( ): . The SI unit of force is the Newton (N). One Newton is defined as the force required to accelerate a 1 kilogram mass by 1 meter per second squared. So, . Step 4: Relate the unit of weight to the unit of force Since weight ( ) is a force, its SI unit must be the same as the SI unit of force. Unit of weight = Unit of mass × Unit of acceleration due to gravity Unit of weight = This combination, , is defined as the Newton (N). Step 5: Evaluate the given options
(1) Kg: This is the SI unit of mass, not weight.
(2) : This is the SI unit of momentum ( ), not weight.
(3) N: This is the SI unit of force, and therefore, of weight.
(4) None of these: Incorrect, as (3) is the correct unit. Therefore, the SI unit of weight is the Newton (N).

Step 1: Understand the units involved.
KWh (Kilowatt-hour) is a unit of energy. It is commonly used to measure electrical energy consumption.
J (Joule) is the standard international (SI) unit of energy. Step 2: Break down KWh into fundamental units. 1 KWh means 1 kilowatt operating for 1 hour.
1 kilowatt (KW) = watts (W)
1 hour (h) = minutes seconds = seconds (s) The relationship between power, energy, and time is: Energy = Power Time. So, 1 KWh = 1 KW 1 h. Step 3: Convert KWh to Joules.
Substitute the values from Step 2:
1 KWh = W s
Recall that 1 Watt (W) = 1 Joule per second (J/s).
So, 1 KWh = (J/s) s
1 KWh = J
Step 4: Express the result in scientific notation.
J can be written as J.
Step 5: Compare the result with the given options.
The calculated value J matches option (1).

Step 1: Define density.
Density is defined as mass per unit volume. Step 2: Recall the SI units for mass and volume.
In the International System of Units (SI):
The SI unit of mass is the kilogram (kg).
The SI unit of length is the meter (m).
The SI unit of volume, derived from length, is cubic meter (m ). Step 3: Determine the SI unit of density.
Since density = mass / volume, the SI unit of density will be the SI unit of mass divided by the SI unit of volume.
SI unit of density = . Step 4: Evaluate the given options.
(1) Kg/cm : This uses kilograms for mass, but cubic centimeters for volume, which is not the SI unit of volume.
(2) Kg/m : This uses kilograms for mass and cubic meters for volume, which are both SI units. This is the correct SI unit for density.
(3) g/m : This uses grams for mass, which is a common unit for mass but not the base SI unit (kilogram is).
(4) g/cm : This uses grams for mass and cubic centimeters for volume. Both are common units but not the primary SI units for density. (2) Kg/m