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The apparent weight of a piece of solid in water is 80 gm-wt and that in kerosene oil is 100 gm-wt (density of kerosene =0•8 gm/cm3)
A. Calculate the weight of the piece of solid in air
B. Calculate its volume
C. What will be the apparent weight of the piece of solid in a liquid of density 1•4 gm/cm3?
NO SPAMS PLEASE
Answers
Answer:
(A) 160 gm-wt
(B) 80 cc
(C) 48 gm-wt
Explanation:
Let the weight of the piece of solid in air is W
Weight of piece of solid in water
= Weight of solid in air - bouyant force in water
= Weight of solid in air - weight of water displaced by the solid
Let the volume of the solid is V
Then the weight of water displaced = V × density of water × g
= V × 1 × g = Vg
Thus
80g= W - Vg .............. (1)
Similarly for kerosene we can write the equation
100g = W - V × 0.8 × g
or, 100g = W - 0.8Vg ........ (2)
Multiplying eq (1) by 0.8 and subtracting it from eq (2)
100g - 64g = 0.2W
or, 0.2W = 32g
or, W = 32g/0.2 = 160g
Therefore, the weight of the piece of solid in air is 160 gm-wt
(B) Putting the value of W in eq (1)
80g = 160g - Vg
or, V = 160 - 80 = 80 cm³
(C) Weight of the liquid displaced = V × density of the liquid × g
= 80 × 1.4 × g = 112g
Therefore, weight of the piece of solid in the liquid
= Weight of the solid - Weight of the liquid displaced
= 160g - 112g
= 48g
Thus, weight of the solid = 48 gm-wt.
Hope this answer is helpful.