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 $${{v}_{T}}$$. 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 [CPMT 1992; CBSE PMT 1992; NCERT 1983; MP PMT 2001]

Question

TuteeHUB · Accepted Answer

$${{v}_{T}}\propto \frac{\eta r}{mg}$$

TuteeHUB · Answer

$${{v}_{T}}\propto \frac{mg}{\eta r}$$

TuteeHUB · Answer

$$({{F}_{2}}-{{F}_{3}})/m$$

TuteeHUB · Answer

$${{v}_{T}}\propto \frac{mgr}{\eta }$$

1.	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 \[{{v}_{T}}\]. 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 [CPMT 1992; CBSE PMT 1992; NCERT 1983; MP PMT 2001]
A.	\[{{v}_{T}}\propto \frac{mg}{\eta r}\]
B.	\[{{v}_{T}}\propto \frac{\eta r}{mg}\]
C.	\[({{F}_{2}}-{{F}_{3}})/m\]
D.	\[{{v}_{T}}\propto \frac{mgr}{\eta }\]
Answer» B. \[{{v}_{T}}\propto \frac{\eta r}{mg}\]

Discussion

No Comment Found

Related MCQs

Reply to Comment