JEE Main 2026 — Jan 23, Shift 2 — Physics solution

JEE Main2026Jan 23, Shift 2Physics

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/cm $^{3}$ respectively. The terminal velocity attained by the sphere is ______ cm/s.

( $π = \frac{22}{7}$ and $g = 10$ m/s $^{2}$ )

A
2.0
B
1.0
C
3.0
D
1.5

Solution

Terminal velocity from Stokes' law:

$V_{T} = \frac{2 r ^{2} g ( ρ _{b} - ρ _{ℓ} )}{9 η}$ .

With $r = 0.1$ cm, $g = 1 0^{3}$ cm/s $^{2}$ (or use CGS: $η = 10$ Poise = 10 g cm $^{- 1}$ s $^{- 1}$ , $g = 1000$ cm/s $^{2}$ , $ρ_{b} - ρ_{ℓ} = 9$ g/cm $^{3}$ ):

$V_{T} = \frac{2 \cdot 0.01 \cdot 1000 \cdot 9}{9 \cdot 10} = \frac{180}{90} = 2$ cm/s.

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