Physics · Mechanical Properties of Matter

JEE Main 2026 — 23 January, Evening Shift — Question 44

A ball of radius r and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time t , given by $\mathrm{t}=\mathrm{A} \rho^{\mathrm{a}} \mathrm{r}^{\mathrm{b}} \eta^{\mathrm{c}} \sigma^{\mathrm{d}}$ , where A is a constant and $\mathrm{a}, \mathrm{b} \mathrm{c}$ and d are integers. The value of $\frac{b+c}{a+d}$ is $\_\_\_\_$ .

Answer: 1

Numerical answer — enter this value.

Step-by-step solution

$\mathrm{T}=\left(\mathrm{ML}^{-3}\right)^{\mathrm{a}} \mathrm{L}^{\mathrm{b}}\left(\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right)^{\mathrm{c}}\left(\mathrm{ML}^{-3}\right)^{\mathrm{d}}$ $\mathrm{T}=\mathrm{M}^{\mathrm{a}+\mathrm{c}+\mathrm{d}} \mathrm{L}^{-3 \mathrm{a}-\mathrm{c}-\mathrm{s} \mathrm{d}+\mathrm{b}} \mathrm{T}^{-\mathrm{c}}$ on comparing $\mathrm{c}=-1 ; \mathrm{a}+\mathrm{c}+\mathrm{d}=0 ;-3 \mathrm{a}-\mathrm{c}-3 \mathrm{~d}+\mathrm{b}=0$ $\mathrm{b}=2 ; \mathrm{a}+\mathrm{d}=1$ $\mathrm{b}+\mathrm{c}=1$

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Exam: JEE Main 2026
Paper: 23 January, Evening Shift
Subject: Physics
Chapter: Mechanical Properties of Matter
Topic: Viscosity

A small metallic sphere of diameter 2 mm and density 10.5 g / cm^3 is dropped in glycerine having viscosity 10 Poise and density 1.5 g /…

Answer: 1

Step-by-step solution

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