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#units and dimensions

3 public questions tagged with this topic.

PHYSICS

Which of the following equations is dimensionally inconsistent?

(a) [v] = [L T^{-1], [u + a t] = [L T^{-1] + [L T^{-2] [T] = [L T^{-1], consistent. (b) [s] = [L], [v t + a t] = [L] + [L T^{-1], inconsistent. (c) [F] = [M L T^{-2], [m v² / r] = [M L² T^{-2] / [L] = [M L T^{-2], consistent. (d) [E] = [M L² T^{-2], [F r] = [M L T^{-2] [L] = [M L² T^{-2], consistent.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Units and Measurements and Physical World, Topic: Dimensional analysis and fundamental principles.

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PHYSICS

The dimensional formula of angular velocity is [T^{-1] . Which quantity shares the same dimensions?

Given: The dimensional formula of angular velocity is [T^{-1] . Which quantity shares the same dimensions? These values define the system as per NCERT data. Formula: (a) [v / r] = [L T^{-1] / [L] = [T^{-1]. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: (b) [a t] = [L T^{-2] [T] = [L T^{-1] . (c) [F / m] = [M L T^{-2] / [M] = [L T^{-2] . (d) [s / t] = [L] / [T] = [L T^{-1] . (a) matches. Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properl

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Units and Measurements and Physical World, Topic: Dimensional analysis and fundamental principles.

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PHYSICS

The dimensional formula of angular acceleration is [T^{-2] . Which quantity shares the same dimensions?

Given: The dimensional formula of angular acceleration is [T^{-2] . Which quantity shares the same dimensions? These values define the system as per NCERT data. Formula: (a) [v² / r²] = [L T^{-1]² / [L]² = [T^{-2]. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: (b) [a / r] = [L T^{-2] / [L] = [T^{-2] . (c) [F / m r] = [M L T^{-2] / [M L] = [T^{-2] . (d) [v t / r] = [L T^{-1] [T] / [L] = [T⁰] . (b) matches (simplest match chosen). Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers l

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Units and Measurements and Physical World, Topic: Dimensional analysis and fundamental principles.

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