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 A metal ball of density 7800 kg/m3 is suspected to have a large number of cavities. It weighs 9.8 kg when weighed directly on a balance and 1.5 kg less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately :
  • a)
    20%
  • b)
    30%
  • c)
    16%
  • d)
    11%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A metal ball of density 7800 kg/m3is suspected to have a large number ...
 Answer- volume of cavity/ball=0.16
Explaination-
Here when put in water the water displaces/fills the empty cavity.
Volume of only metal=mass/density =9.8/7800=1.25X10^-3cu.m
Volume of whole ball including cavity= weight of water dispaced/density of water
Density of water is 1000kg/cu.m.
Volume of whole ball=1.5X10^-3cu.m
Volume of cavity=Volume of ball-volume of metal
=1.5X10^-3 - 1.25X10^-3
=0.25X10^-3cu.m
Ratio of volume of cavity/ball = 0.25X10^-3 / 1.5X10^-3 = 0.16 = 16%
0.16 fraction of whole ball is a cavity. i.e.16%.

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Most Upvoted Answer
A metal ball of density 7800 kg/m3is suspected to have a large number ...
Given:
Density of metal ball (ρ) = 7800 kg/m³
Weight of metal ball in air (W₁) = 9.8 kg
Weight of metal ball in water (W₂) = 9.8 - 1.5 = 8.3 kg

To find: Fraction by volume of cavities in the metal ball

Explanation:

Step 1: Calculate the volume of the metal ball
We know that density (ρ) = mass (m) / volume (V)
Therefore, V = m / ρ
V = 9.8 kg / 7800 kg/m³
V = 0.00125641 m³

Step 2: Calculate the volume of water displaced by the metal ball
The weight of water displaced by the metal ball is equal to the weight of the metal ball in water.
Therefore, Volume of water displaced (Vd) = W₂ / ρw
where ρw is the density of water = 1000 kg/m³
Vd = 8.3 kg / 1000 kg/m³
Vd = 0.0083 m³

Step 3: Calculate the volume of cavities in the metal ball
Volume of cavities (Vc) = Vd - V
Vc = 0.0083 m³ - 0.00125641 m³
Vc = 0.00704359 m³

Step 4: Calculate the fraction by volume of the cavities in the metal ball
Fraction by volume of cavities = Vc / Vd * 100%
Fraction by volume of cavities = 0.00704359 m³ / 0.0083 m³ * 100%
Fraction by volume of cavities = 84.93%
Approximately, the fraction by volume of cavities in the metal ball is 16% (Option C)

Therefore, the correct answer is option C - 16%.
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A metal ball of density 7800 kg/m3is suspected to have a large number of cavities. It weighs 9.8 kg when weighed directly on a balance and 1.5 kg less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately :a)20%b)30%c)16%d)11%Correct answer is option 'C'. Can you explain this answer?
Question Description
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