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Q.

A spherical body of mass m and radius r is allowed to faII 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   can be represented by

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a

mr26πη

b

6πmrηg2

c

m6πηrV

d

None of the above

answer is D.

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Detailed Solution

The dimension of modulus of rigidity [η]=ML−1T−1∴ mr26πη=ML2ML−1T−1=L3T16πmrηg21/2=MLML−1T−11/2LT−2=ML−1T3/2m6πηrv=MML−1T−1LLT−1=L−1T2Hence none of the given expressions have the dimensions of time
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A spherical body of mass m and radius r is allowed to faII 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   can be represented by