KVPY 2020-21 SB SX Exam Previous Papers

Question : 37 of 120

Marks: +1, -0

The time period of a body undergoing simple harmonic motion is given by

{T}={p}^{{a}} {D}^{{b}} {S}^{{c}}

, where

{p}

is the pressure,

{D}

is density and

{S}

is surface tension. The values of a,

{b}

and

{c}

respectively are

Solution:

[{T}']=[{m}^{{a}} {L}^{-{a}} {T}^{-2 {a}} \;\;{m}^{{b}} {L}^{-3 {b}} {m}^{{c}} {T}^{-2 {c}}]

[{T}']=[{m}^{{a}+{b}+{c}} {L}^{-{a}-3 {b}} {T}^{-2 {a}-2 {c}}]

{a}+{b}+{c}=0

-a-3 b=0

-2 a-2 c=1

On solving

{a}={-3}/{2}, {b}={1}/{2}, {c}=1

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