Define 1 kgf and How is it related to the si unit class 11 physics CBSE

(a) Define 1 kgf. How is it related to the S.I unit of force?
(b) Calculate the refractive index of air with respect to diamond if the refractive index of diamond with respect to air is 2.4.

Physics provides us with precise definitions and relationships between units that help us understand fundamental concepts. In this discussion, we will explore the definition of 1 kilogram-force (kgf), its relation to the S.I unit of force, and the calculation of the refractive index of air with respect to diamond.

(a) Definition of 1 kgf and Its Relation to the S.I Unit of Force

Definition of 1 kgf

1 kilogram-force (kgf) is the force exerted by a 1 kg mass when placed under standard gravitational acceleration (g = 9.8 m/s²). It is a unit of force commonly used in practical applications before the widespread adoption of the S.I unit of force.

Mathematically,

1 kgf=Mass×Acceleration due to gravity1 \text{ kgf} = \text{Mass} \times \text{Acceleration due to gravity} 1 kgf=1 kg×9.8 m/s²1 \text{ kgf} = 1 \text{ kg} \times 9.8 \text{ m/s²} 1 kgf=9.8 N1 \text{ kgf} = 9.8 \text{ N}

Relation to the S.I Unit of Force

The S.I unit of force is the Newton (N), which is defined as the force required to accelerate a 1 kg mass by 1 m/s². The relationship between kgf and Newton is:

1 kgf=9.8 N1 \text{ kgf} = 9.8 \text{ N}

Thus, kilogram-force (kgf) is a non-S.I unit, while Newton (N) is the standard S.I unit of force.

(b) Calculation of the Refractive Index of Air with Respect to Diamond

Understanding Refractive Index

The refractive index (n) of a medium determines how much light bends when it passes from one medium to another. It is calculated using the formula:

n1,2=1n2,1n_{1,2} = \frac{1}{n_{2,1}}

where:

• n1,2n_{1,2} is the refractive index of medium 1 (air) with respect to medium 2 (diamond).
• n2,1n_{2,1} is the refractive index of medium 2 (diamond) with respect to medium 1 (air), given as 2.4.

Calculation

Using the formula:

nair, diamond=1ndiamond, air=12.4n_{\text{air, diamond}} = \frac{1}{n_{\text{diamond, air}}} = \frac{1}{2.4} nair, diamond=0.42n_{\text{air, diamond}} = 0.42

• 1 kgf is defined as the force exerted by a 1 kg mass under gravity and is equal to 9.8 N in S.I units.
• The refractive index of air with respect to diamond is 0.42, which means that light speeds up when moving from diamond to air.

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