Answer to Question #152628 in Classical Mechanics for Isurini Sirisena

Question

A ball bearing of mass 180 g is hung on a thread in oil of density 800 kg m−3. Calculate the tension in the string if the density of the ball bearing is 8000 kg m−3.

Answer 1

Answer

We can calculate tension as below process

Volume of ball bearing = mass/density

$= 0.180kg/(8000 kg/m³)$

$= 2.25\times10^{-5} m³$

Volume of oil displaced

$= 2.25\times10^{-5 }m³$

Mass of loil displaced

$= volume \times density$

$= 2.25\times10^{-5 }\times800$

$= 0.018kg$

Buoyancy force

= weight of liquid displaced

= mg

$= 0.018 \times9.81$

= 0.177N (upwards)

Weight of ball bearing

= mg

$= 0.18 \times9.81$

= 1.77N (downwards)

so Tension = weight - buoyancy

= 1.77 - 0.177

= 1.6N