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BITSAT 2011

Exam: BITSAT
Year: 2011
Subject: Physics
Chapter: Units and Dimensions

BITSAT 2011 · Physics · Units and Dimensions

If T=2 π ML^ 3 3 Yq then find the dimensions of q. Where T is the...

If

\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{ML}^{3}}{3 \mathrm{Yq}}}

then find the dimensions of q. Where

\mathrm{T}

is the time period of bar of mass

\mathrm{M}

length

\mathrm{L}

and Young modulus

\mathrm{Y}

.

Options

A $[\mathrm{L}]$
B $\left[\mathrm{L}^{2}\right]$
C $\left[\mathrm{L}^{4}\right]$
D $\left[\mathrm{L}^{3}\right]$

Correct answer

C. $\left[\mathrm{L}^{4}\right]$

Step-by-step solution

\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{ML}^{3}}{3 \mathrm{Yq}}},

writing dimensions of both the sides, we get

[\mathrm{T}]=\left[\frac{\mathrm{ML}^{3}}{\mathrm{ML}^{-1} \mathrm{ T}^{-2} \mathrm{q}}\right]^{1 / 2}

or \quad q= \left[L^{4}\right]

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