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QJEEM24Phb03e: JEE Main 2024 Physics - Class 11 JEEM24Phb03e Solution: A small spherical ball of radius , falling through a viscous…

A small spherical ball of radius rr , falling through a viscous medium of negligible density has terminal velocity ' vv '. Another ball of the same mass but of radius 2r2 r , falling through the same viscous medium will have terminal velocity:

Multiple Choice Options

  • A 4v4 \mathrm{v}
  • B 2 V2 \mathrm{~V}
  • C v4\frac{v}{4}
  • D v2\frac{\mathrm{v}}{2}

Step-by-Step Verified Solution

Since density is negligible hence Buoyancy force will be negligible

At terminal velocity.

Mg=6πηrv\mathrm{Mg} =6 \pi \eta \mathrm{rv}

V∝1r\mathrm{V} \propto \frac{1}{\mathrm{r}} \quad (as mass is constant)

Now, vv′=r′r\frac{\mathrm{v}}{\mathrm{v}^{\prime}}=\frac{\mathrm{r}^{\prime}}{\mathrm{r}}

r′=2rr^{\prime}=2 \mathrm{r}

So, v′=v2v^{\prime}=\frac{v}{2}

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