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Question

Two liquids of densities $$d_{1}$$ and $$d_{2}$$ are flowing in identical capillaries under same pressure difference, If $$t_{1}$$ and $$t_{2}$$ are the time taken for the flow of equal quantities of liquids, then the ratio of coefficients of viscosities of liquids must be -


A
d1d2t1t2
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B
d1t1d2t2
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C
d1t2d2t1
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D
d1t1d2t2
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Solution

The correct option is B $$\displaystyle \frac{d_{1}t_{1}}{d_{2}t_{2}}$$
we know that from the concept of Reylonld's number $$Re=\dfrac { dvt }{ \mu  }$$
given that fluid is flowing in identical capillaries under same pressure difference, so $${Re}_{1}={Re}_{2}$$
$$\dfrac { { d }_{ 1 }\times v\times { t }_{ 1 } }{ { \mu  }_{ 1 } } =\dfrac { { d }_{ 2 }\times { v\times  }{ t }_{ 2 } }{ { \mu  }_{ 2 } } $$
$$\dfrac { { \mu  }_{ 1 } }{ { \mu  }_{ 2 } } =\dfrac { { d }_{ 1 }{ t }_{ 1 } }{ { d }_{ 2 }{ t }_{ 2 } }$$

Physics

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