Fluid Mechanics

JEE Main level, single correct, medium

167 of 192

Question 167 of 192

In the experiment for measurement of viscosity ' η\eta ' of given liquid with a ball having radius RR, consider following statements.
A. Graph between terminal velocity V and R will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of η\eta will change.
Choose the correct answer from the options given below:

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Answer: (C) { }^{} A, C and D Only

The terminal velocity of ball of radius RR inside a liquid of viscosity η\eta can be written as VT=2R2gn(σ−ρ)V_T=\frac{2 R^2 g}{n}(\sigma-\rho), where σ\sigma is the density of ball and δ\delta is the density of the liquid.
Hence,
AA is correct since VT∝R2V_T \propto R^2 gives a parabola on a graph
CC is correct since VTα1ηV_T \alpha \frac{1}{\eta} and η\eta varies with temperature
DD is correct since VTα(σ−ρ)V_T \alpha(\sigma-\rho) i.e., varies with density of liquid.

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