Dimensional Analysis and its Applications NEET Questions

Physics - Physics and Measurement
Dimensional Analysis and its Applications

Dimensional Analysis and its Applications MCQ Questions


13.
For T = 2π√(l/g), dimensional check of √(l/g) gives:
A.
[L/LT⁻²]½ = [T²]½ = [T]
B.
[L/LT⁻²]½ = [L²T⁻²]½ = [LT⁻¹]
C.
[L/LT⁻²]½ = [T⁻²]½ = [T⁻¹]
D.
[L/LT⁻²]½ = [L²]½ = [L]
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ANSWER :
A. [L/LT⁻²]½ = [T²]½ = [T]
14.
The equation v² = u² + 2as is verified dimensionally. What are the dimensions of [2as]?
A.
[LT⁻¹]
B.
[L²T⁻²] — same as [v²] and [u²]
C.
[L²T⁻¹]
D.
[MLT⁻²]
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ANSWER :
B. [L²T⁻²] — same as [v²] and [u²]
15.
For Newton's law of gravitation F = Gm₁m₂/r², if we check dimensions of G using this equation:
A.
[G] = [F][r²]/[m₁m₂] = [M⁻¹L³T⁻²]
B.
[G] = [F][r²]/[m₁m₂] = [ML³T⁻²]
C.
[G] = [F][m₁m₂]/[r²] = [M³LT⁻²]
D.
[G] = [F]/[r²m₁m₂] = [M⁻¹L⁻¹T⁻²]
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ANSWER :
A. [G] = [F][r²]/[m₁m₂] = [M⁻¹L³T⁻²]
16.
Hooke's law: F = −kx where k is spring constant, x is extension. Dimensions of k are:
A.
[MT⁻²]
B.
[MLT⁻²]
C.
[ML⁻¹T⁻²]
D.
[ML²T⁻²]
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ANSWER :
A. [MT⁻²]
17.
For simple harmonic motion: ω = √(k/m), where ω is angular frequency, k is spring constant, m is mass. Check dimensions of √(k/m):
A.
[MT⁻²/M]½ = [T⁻²]½ = [T⁻¹] = [ω]
B.
[MT⁻²/M]½ = [T⁻¹]½ = [T(-½)]
C.
[k/m]½ = [ML T⁻²]½ = [M½L½T⁻¹]
D.
[k/m]½ = [MT⁻²/M]½ = [T²]½ = [T]
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ANSWER :
A. [MT⁻²/M]½ = [T⁻²]½ = [T⁻¹] = [ω]
18.
The ideal gas law PV = nRT. If P=[ML⁻¹T⁻²], V=[L³], n=dimensionless, T=[K], then dimensions of R are:
A.
[ML²T⁻²K⁻¹mol⁻¹]
B.
[ML²T⁻²K⁻¹]
C.
[ML⁻¹T⁻²K⁻¹]
D.
[M⁰L²T⁻²K⁻¹]
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ANSWER :
A. [ML²T⁻²K⁻¹mol⁻¹]
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