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A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity `eta`. After some time the velocity of the ball attains a constant value known as terminal velocity `upsilon_T`. The terminal velocity depends on (i) the mass of the ball m (ii) `eta`, (iii) r and (iv) acceleration due to gravity g . Which of the following relations is dimensionally correct?A. `v_Tprop(mg)/(etar)`B. `v_Tprop(etar)/(mg)`C. `v_Tetarmg`D. `v_Tprop(mgr)/(eta)` |
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Answer» Correct Answer - A by subsituting dimension of each quantity is R.H.S of option (a) we get `[(mg)/(etar)]=[(MxxLT^-2)/(ML^-1T^-1xxL)]=[LT^-1]`. This option gives the dimension of velocity. |
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