IJMB 2024 PHYSICS QUESTIONS
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IJMB PHYSICS
NUMBER 1
1i
1. *Checking Consistency of Equations*: Dimensional analysis helps verify the correctness of physical equations by ensuring that both sides of an equation have the same dimensional formula. This can identify potential errors in derivations and calculations.
2. *Deriving Relationships Between Physical Quantities*: Dimensional analysis can be used to derive equations that relate different physical quantities. By analyzing the dimensions involved, it’s possible to determine the form of a relationship even without detailed knowledge of the underlying mechanisms.
3. *Converting Units*: Dimensional analysis simplifies the process of converting between different units of measurement. By treating units as algebraic quantities, it provides a systematic method for converting complex expressions from one unit system to another.
IJMBE PHYSICS
3i
Triangular Law of Vector Composition
The triangular law of vector composition states that if two vectors are represented as two sides of a triangle taken in order, their resultant vector is represented by the third side of the triangle taken in the opposite order.
Parallelogram Law of Vector Composition
The parallelogram law of vector composition states that if two vectors are represented as adjacent sides of a parallelogram, their resultant vector is represented by the diagonal of the parallelogram that starts from the same point.
No 13B
The coefficient of cubic expansivity (γ) is defined as:
γ = (1 / V₀) × (ΔV / ΔT)
where:
γ = coefficient of cubic expansivity
V₀ = original volume
ΔV = change in volume
ΔT = change in temperature
The coefficient of linear expansivity (α) is defined as:
α = (1 / L₀) × (ΔL / ΔT)
where:
α = coefficient of linear expansivity
L₀ = original length
ΔL = change in length
ΔT = change in temperature
Now, let’s consider a cube with sides of length L₀. The volume V₀ is:
V₀ = L₀³
When the temperature changes by ΔT, the length changes by ΔL, and the volume changes by ΔV. The new volume V is:
V = (L₀ + ΔL)³
Using the binomial theorem, we can expand this expression:
V = L₀³ + 3L₀²ΔL + 3L₀(ΔL)² + (ΔL)³
Since ΔL is small compared to L₀, we can neglect the higher-order terms (ΔL)² and (ΔL)³. Then:
V = L₀³ + 3L₀²ΔL
The change in volume ΔV is:
ΔV = V – V₀ = 3L₀²ΔL
Now, we can express ΔV in terms of α:
ΔV = 3L₀²αΔT
Substituting this into the definition of γ, we get:
γ = (1 / V₀) × (3L₀²αΔT) / ΔT
Simplifying, we get:
γ = 3α
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