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?

Question

Answer

Dimensions of Energy:

Energy is defined as the capacity to do work or the ability to cause changes in a system. In the context of fundamental physical quantities, energy can be expressed in terms of force [F], acceleration [A], and time [T].

Given Fundamental Quantities:
- Force [F]
- Acceleration [A]
- Time [T]

Formula for Energy:
Energy (E) = Force (F) x Distance (D)

Dimensions of Energy:
- Energy = Force x Distance
- Distance = Acceleration x Time^2 (from the formula for acceleration)
- Therefore, Energy = Force x (Acceleration x Time^2)
- Substituting the fundamental quantities, Energy = [F][A][T^2]

Therefore, the correct dimensions of energy in terms of force [F], acceleration [A], and time [T] are [F][A][T^2], which corresponds to option 'B'.

Answer

Energy, E ∝ F^aA^bT^c

[E] = [F^a][A^b][T^c]

⇒ [ML²T⁻²] = [MLT⁻²]^a[LT⁻²]^b[T]^c

[ML²T⁻²] = [M^aL^a+bT^−2a−2b+c]

Comparing dimensions on both sides.

⇒ a = 1 ; a + b = 2 and −2 = −2a − 2b + c

⇒ b = 1 ⇒ −2 = −2 −2 + c

⇒ c = 2

[E] = [F AT²]

Similar NEET Doubts

If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

A2.8. If density d, acceleration a and force f are taken as basic quantities. then time period has dimensions?Sol) {4}1)1/6 in F2)-1/6 in D3)-2/3 in a4) all the above are true?

A physical quantity depends on quantities y and z as follows x=Ay BtanCz where a b c are constants . Which of the following have different dimensions? A ) x and b B ) c and z^-1 C)y and b/a D) x and a?

A physical quantity x depends on quantities y and z as x = Ay B sin (C z), where A, B, and C are constants. Which of the following have same dimensions? (1) x and Ay (2) x and B (3) C and z-1 (4) All of the above?

A physical quantity x depends on quantities y and z as follows: x= Ay+BtanCz , where A,B and C are constants. which of the following do not have the same dimensions.

Top Courses for NEETView all

Biology Class 11

Daily Test for NEET Preparation

NEET Mock Test Series 2025

Topic-wise MCQ Tests for NEET

Physics Class 11

Top Courses for NEET

Top Courses for NEET

Suggested Free Tests

Related Content

About NEET

NEET Preparation Material

How to Prepare for NEET Exam?

NCERT Based Study Material

NEET Mock Tests

Other Popular Exams

Company