Question

A solid sphere of mass 8.6 kg, made of metal whose density is 3,400 kg/, hangs by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 38 N. The density of the liquid is closest to which one of the following values?A) 1900 kg/m³B) 1600 kg/m³C) 1700 kg/m³D) 1400 kg/m³E) 1500 kg/m³

Answer 1

A.
`1900 kg/m^3`

Step-by-step explanation:

We are given that

`m=8.6 kg`

Density,
`\rho_s=3400 kg/m^3`

Tension,T=38 N

We have to find the density of liquid.

`T=mg-\rho_l Vg`

`g=9.8 m/s^2`

Volume,V=
`(m)/(\rho_s)`

`38=8.6* 9.8-\rho_l* (8.6)/(3400)* 9.8`

`\rho_l* (8.6)/(3400)* 9.8=8.6* 9.8-38`

`\rho_l=((8.6* 9.8-38)* 3400)/(8.6* 9.8)`

`\rho_l=1867kg/m^3\approx 1900 kg/m^3`

Option A is true.