In the experiment for measurement of viscosity ' $\eta$ ' of given liquid with a ball having radius $R$,…

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:
  1. ${ }_{} \mathrm{A}, \mathrm{B}$ and E Only
  2. B, D and E Only
  3. ${ }^{}$ A, C and D Only
  4. C, D and E Only

Solution

The terminal velocity of ball of radius $R$ inside a liquid of viscosity $\eta$ can be written as $V_T=\frac{2 R^2 g}{3n}(\sigma-\rho)$, 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.

Asked in: JEE Main 2025 (28 Jan Shift 1)

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