Q62 / 75 · JEE Main 2025 (28 Jan Shift 1) · Physics

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:

  • A
    ${ }_{} \mathrm{A}, \mathrm{B}$ and E Only
  • B
    B, D and E Only
  • Correct answer
    C
    ${ }^{}$ A, C and D Only
  • D
    C, D and E Only

Solution

The terminal velocity of ball of radius $R$ inside a liquid of viscosity $\eta$ can be written as $V_T=\frac{2 R^2 g}{n}(\sigma-\rho)$, 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, the correct answer is option: 'C'.

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