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If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.
- a)[F][A][T]
- b)[F][A][T2]
- c)[F][A][T−1]
- d)[F][A−1][T]
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If force [F], acceleration [A] and time [T] are chosen as the fundamen...
To find the dimensions of energy, we can use the fundamental physical quantities given:
Energy = Force × Distance
Since force is given as [F], acceleration can be expressed as [A] = [F]/[T]. Therefore, the dimensions of acceleration are [F][T]⁻¹.
Now, substituting this value for acceleration in the equation for energy:
Energy = Force × Distance = [F][T]⁻¹ × Distance
To simplify further, we can express distance as [D] = [A] × [T]² = ([F]/[T]) × [T]² = [F][T]².
Substituting this value for distance in the equation for energy:
Energy = [F][T]⁻¹ × [D] = [F][T]⁻¹ × [F][T]² = [F]²[T]¹
Therefore, the dimensions of energy are [F]²[T]¹.
So, the correct option is:
a) [F][A][T]
Energy = Force × Distance
Since force is given as [F], acceleration can be expressed as [A] = [F]/[T]. Therefore, the dimensions of acceleration are [F][T]⁻¹.
Now, substituting this value for acceleration in the equation for energy:
Energy = Force × Distance = [F][T]⁻¹ × Distance
To simplify further, we can express distance as [D] = [A] × [T]² = ([F]/[T]) × [T]² = [F][T]².
Substituting this value for distance in the equation for energy:
Energy = [F][T]⁻¹ × [D] = [F][T]⁻¹ × [F][T]² = [F]²[T]¹
Therefore, the dimensions of energy are [F]²[T]¹.
So, the correct option is:
a) [F][A][T]
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Community Answer
If force [F], acceleration [A] and time [T] are chosen as the fundamen...
On comparing powers of [M]
α = 1
On comparing powers of [L]
α + b = 2
⇒ 1 + b = 2
⇒ b = 1
On comparing powers of [T]
−2α − 2b + c = −2
⇒ −2 − 2 + c = −2
⇒ c = 2
[Energy] = [F] [A] [T2]
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