A researcher lifts a sample of porous rock straight upward through ethanol (density )…

PHYSICS · Subjective · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

A researcher lifts a

2.5\,\text{kg}

sample of porous rock straight upward through ethanol (density

790\,\text{kg}\!\cdot\!\text{m}^{-3}

) using a light string. While passing through the fluid, the rock experiences an upward buoyant force of

6.8\,\text{N}

. If the lift motor produces a time-dependent upward acceleration given by

a(t)=0.40t

in SI units (for

0\le t\le2.0\,\text{s}

), derive an expression for the tension

T(t)

in the string and evaluate

T

t=2.0\,\text{s}