First slide

Viscosity

Question

A small metal sphere falls down in a liquid with terminal velocity when the viscous force on it and its weight are in the ratio 2:5. Then the density of the sphere is

Moderate

A

Equal to that of the liquid
B

1.66 times that of the liquid
C

2.5 times to that of the liquid
D

3 times that of the liquid

Solution

$c o n d i t i o n f o r t e r m i n a l v e l o c i t y W = F_{b} + F_{v} h e r e b u o y a n t f o r c e F_{b} = W - F_{v} s o F_{b} = 5 F - 2 F = 3 F W = V d_{s} g = 5 F a n d F_{b} = V d_{l} g = 3 F d_{s} = \frac{5}{3} d_{l}$

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