A spherical body of mass m and radius r is allowed to fall in a medium of viscosity η. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v) is called time constant (τ).Dimensionally, τ can be represented by
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a
mr26πη
b
6πmrηg2
c
m6πηrv
d
None of these
answer is D.
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Detailed Solution
mr26πη=ML2ML−1T−1=L3T As we have [η]=ML−1T−16πmrηg21/2=MLML−1T−1L2T−41/2m6πηrv=MML−1T−1LLT−1=L−1T2Thus, none of the given expressions have the dimensions of time constant.