A metal ball of density 7800 kg / m 3 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 :

Question

A metal ball of density 7800 kg / m 3 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 %

Tardigrade Admin · Accepted Answer

∴ Volume where metal is present =(9.8/7800)=1.256 × 10-3 Buoyancy =v ρ g=1.5 g ⇒ v × 1000=1.5 v=1.5 × 10-3 fraction of volume =(1.5 × 10-3-1.256 × 10-3/1.5 × 10-3) × 100=16 %

Q. A metal ball of density $7800 k g / m^{3}$ is suspected to have a large number of cavities. It weighs $9.8 k g$ when weighed directly on a balance and $1.5 k g$ less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately :

$20%$

$30%$

$16%$

$11%$

$∴$ Volume where metal is present
$= \frac{9.8}{7800} = 1.256 \times 1 0^{- 3}$
Buoyancy $= v ρ g = 1.5 g$
$\Rightarrow v \times 1000 = 1.5$
$v = 1.5 \times 1 0^{- 3}$
fraction of volume
$= \frac{1.5 \times 1 0 ^{- 3} - 1.256 \times 1 0 ^{- 3}}{1.5 \times 1 0 ^{- 3}} \times 100 = 16%$

Q. A metal ball of density 7800kg/m3 is suspected to have a large number of cavities. It weighs 9.8kg when weighed directly on a balance and 1.5kg less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately :

20%

30%

16%

11%