a
(a)

According to poiseuille's equation, Volume of liquid flowing per second in a capillary tube is given by

\(Q =\frac{ V }{ t }=\frac{\pi r ^4 \Delta P }{8 \eta L }\)

So mass of liquid flowing in a capillary tube is given by

\(Q _{ m }=\frac{ m }{ t }=\frac{\pi r ^4 \Delta P }{8 \eta L } d\)

\(\Rightarrow \frac{ m _1}{ t _1}=\frac{\pi r ^4 \Delta P }{8 \eta_1 L } d _1 \ldots(I)\)

\(\Rightarrow \frac{ m _2}{ t _2}=\frac{\pi r ^4 \Delta P }{8 \eta_2 L } d _2 \ldots(II)\)

Dividing \((I)\) by \((II)\), we have

\(\frac{ t _2}{ t _1}=\frac{ d _1}{ d _2} \times \frac{\eta_2}{\eta_1}\)

\(\Rightarrow \frac{\eta_1}{\eta_2}=\frac{ d _1 t _1}{ d _2 t _2}\)