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  • A spherical object of mass 1 kg and radius is falling vertically downward inside viscous liquid in gravity free space. At a certain instant, the velocity of the sphere is 2m/s. If the coefficient o

A spherical object of mass 1 kg and radius is falling vertically downward inside viscous liquid in gravity free space. At a certain instant, the velocity of the sphere is 2m/s. If the coefficient of viscosity of the liquid is \frac{1}{6\pi}SI units, then velocity of ball will become 0.5 m/s after a time.

Option: 1

ln(4)sec


Option: 2

2ln(4)sec


Option: 3

3ln(4)sec


Option: 4

None


Answers (1)

best_answer

According to the formula of stroke's

\begin{aligned} F=(6 \pi \eta \gamma v) & =6 \pi\left(\frac{1}{6 \pi}\right) \times 1 \times v \\ & =v \end{aligned}

\\\therefore\ Retardation,\ a=-\frac{f}{m}=-v\\ or\ \ \ \frac{d v}{d t}=-v

Integrating both sides, we get

\begin{aligned} \int_0^t d t & =-\int_2^{0.5} \frac{d v}{v} \\ \left.t\right|_0 ^t & =-[\ln v]_2^{0.5} \\ t & =-[\ln 0.5-\ln 2] \\ t & =-\left[\ln \left(\frac{1}{4}\right)=\ln (4) \mathrm{sec}\right. \end{aligned}

Posted by

Divya Prakash Singh

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