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}

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