# A body weighs 160 grams in air,130 grams in water and 136 grams in oil.what is the specific gravity of oil?

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Let the density of the body = p kg/m³

its volume = v m³

weight of body in a medium = (density of body-density of medium)×v×g

__Case:1__

weight in air = 160g = 0.16kg × g m/s² (g=acceleration due to gravity)

density of air ≈ 0

Thus

0.16×g = (p-0)vg

⇒v = 0.16/p

__Case:2__

weight in water = 130g = 0.13kg × g m/s²

density of water = w kg/m³

Thus

0.13 × g = (p - w)vg

⇒p-w = 0.13/v

⇒p-w = 0.13/(0.16/p)

⇒p-w = 0.13p/0.16

⇒p-w = 13p/16

⇒p - 13p/16 -w = 0

⇒3p/16 = w

⇒p = 16w/3

__Case:3__

weight in oil = 136g = 0.136kg × g m/s²

density of oil = d kg/m³

Thus

0.136 × g = (p - d)vg

⇒0.136 = (p-d)v

⇒0.136 = (p-d)(0.16/p)

⇒0.136 = (0.16)

⇒ 0.136/0.16 = 1-

⇒0.85 = 1 -

⇒0.85 = 1 -

But accrding to defination of specific gravity, specific gravity of oil =

⇒ = 1 - 0.85

⇒ = 0.15

⇒ = ×0.15

⇒ =

⇒ =__0.8__

its volume = v m³

weight of body in a medium = (density of body-density of medium)×v×g

weight in air = 160g = 0.16kg × g m/s² (g=acceleration due to gravity)

density of air ≈ 0

Thus

0.16×g = (p-0)vg

⇒v = 0.16/p

density of water = w kg/m³

Thus

0.13 × g = (p - w)vg

⇒p-w = 0.13/v

⇒p-w = 0.13/(0.16/p)

⇒p-w = 0.13p/0.16

⇒p-w = 13p/16

⇒p - 13p/16 -w = 0

⇒3p/16 = w

⇒p = 16w/3

weight in oil = 136g = 0.136kg × g m/s²

density of oil = d kg/m³

Thus

0.136 × g = (p - d)vg

⇒0.136 = (p-d)v

⇒0.136 = (p-d)(0.16/p)

⇒0.136 = (0.16)

⇒ 0.136/0.16 = 1-

⇒0.85 = 1 -

⇒0.85 = 1 -

But accrding to defination of specific gravity, specific gravity of oil =

⇒ = 1 - 0.85

⇒ = 0.15

⇒ = ×0.15

⇒ =

⇒ =

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Specific gravity of a medium = density of the medium / density of water

= ρ = ρ_{medium} / ρ_{water}

= ρ = ρ_{medium} / ρ_{water}