Assertion: In the relation (f=(1)/(2 l) (T)/(μ) ), where symbols have standard meaning, (μ) represent linear mass density. Reason : The frequency has the dimensions of inverse of time.

Correct answer: B. If both assertion and reason are true but reason is not the correct explanation of assertion From, f=(1)/(2 l) (T)/(μ) , f^2=(T)/(4 l^2 μ) or, aligned μ & =(T)/(4 l^2 f^2)= [MLT^ -2 ] L^2 T^ -2 = M L & = Mass length = linear mass density. aligned

AIIMS 2008

Exam: AIIMS
Year: 2008
Subject: Physics
Chapter: Units and Dimensions

AIIMS 2008 · Physics · Units and Dimensions

Assertion: In the relation (f=(1)/(2 l) (T)/(μ) ), where symbols...

Assertion: In the relation (f=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}), where symbols have standard meaning, (\mu) represent linear mass density. Reason : The frequency has the dimensions of inverse of time.

Options

AIf both assertion and reason are true and reason is the correct explanation of assertion
BIf both assertion and reason are true but reason is not the correct explanation of assertion
CIf assertion is true but reason is false
DIf both assertion and reason are false.

Correct answer

B. If both assertion and reason are true but reason is not the correct explanation of assertion

Step-by-step solution

From,

f=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}, f^2=\frac{T}{4 l^2 \mu}

or,

\begin{aligned} \mu & =\frac{T}{4 l^2 f^2}=\frac{\left[\mathrm{MLT}^{-2}\right]}{\mathrm{L}^2 \mathrm{ T}^{-2}}=\frac{\mathrm{M}}{\mathrm{L}} \\ & =\frac{\text{ Mass }}{\text{ length }}=\text{ linear mass density. }\end{aligned}

Practice Units and Dimensions on Quantrex Academy →

More from Units and Dimensions

If the errors involved in the measurement of a side and the mass of a cube are 2\% and… MHT CET Medical 2026 If the mass of the object is measured as m = (7 ∓ 0.14) kg and the density is measured as… MHT CET Medical 2026 Consider that σ_s , k_B , b represent Stefan-Boltzmann constant, Boltzmann constant and… NEET 2026 The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the… NEET 2026 Each side of a metallic cube of mass 5.580 kg is measured to be 9.0 cm. Keeping the… NEET 2026 A physical quantity P is related to four observations a, b, c and d as follows : P=a^3… NEET 2025 A balloon is made of a material of surface tension S and its inflation outlet (from where… NEET 2025 The quantities which have the same dimensions as those of solid angle are: NEET 2024 Full Units and Dimensions list All AIIMS PYQs