JEE Mains · Physics · STD 11 - Fluid mechanics
- JEE Mains 2025
- Hard
- MCQ
In the experiment for measurement of viscosity ' \(\eta\) ' of given liquid with a ball having radius \(R\), 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 \(\eta\) will change.
Choose the correct answer from the options given below:
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) A, C and D Only
Step-by-step Solution
Detailed explanation
The terminal velocity of ball of radius \(R\) inside a liquid of viscosity \(\eta\) can be written as \(V_T=\frac{2 R^2 g}{n}(\sigma-\rho)\), where \(\sigma\) is the density of ball and \(\delta\) is the density of the liquid.
Hence,
\(A\) is correct since \(V_T \propto R^2\) gives a parabola on a graph
\(C\) is correct since \(V_T \alpha \frac{1}{\eta}\) and \(\eta\) varies with temperature
\(D\) is correct since \(V_T \alpha(\sigma-\rho)\) i.e., varies with density of liquid.
Hence,
\(A\) is correct since \(V_T \propto R^2\) gives a parabola on a graph
\(C\) is correct since \(V_T \alpha \frac{1}{\eta}\) and \(\eta\) varies with temperature
\(D\) is correct since \(V_T \alpha(\sigma-\rho)\) i.e., varies with density of liquid.
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