Question #152628

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.


1
Expert's answer
2020-12-24T11:42:43-0500

Answer

We can calculate tension as below process

Volume of ball bearing = mass/density

=0.180kg/(8000kg/m3)= 0.180kg/(8000 kg/m³)

=2.25×105m3= 2.25\times10^{-5} m³

Volume of oil displaced

=2.25×105m3= 2.25\times10^{-5 }m³


Mass of loil displaced

=volume×density= volume \times density

=2.25×105×800= 2.25\times10^{-5 }\times800

=0.018kg= 0.018kg

Buoyancy force

= weight of liquid displaced

= mg

=0.018×9.81= 0.018 \times9.81

= 0.177N (upwards)


Weight of ball bearing

= mg

=0.18×9.81= 0.18 \times9.81

= 1.77N (downwards)


so Tension = weight - buoyancy

= 1.77 - 0.177

= 1.6N


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