A stone of volume 1.42 $\times$ 10^-2 m³ lies at the bottom of a freshwater lake.If the rock's specific gravity is 3.5,the work required to lift it 1 m through the water is approximately A)487 J B)139 J C)348 J D)223 J E)469 J

Question

Quizplus · Accepted Answer

The weight of the stone is given by:
$W = mg = ho_{stone} V_{stone} g = ho_{water} V_{stone} g \frac{ho_{stone}}{ho_{water}}$
where $ho_{water}$ is the density of water and $g$ is the acceleration due to gravity. Substituting the given values, we get:
$W = (1000 	ext{ kg/m}^3) (\pi/6) (1.42	imes10^{-10}	ext{ m})^3 g (3.5) \approx 5.65 	imes 10^{-4} 	ext{ N}$
To lift the stone by 1 m, we need to do work:
$W_{lift} = Wd = (5.65 	imes 10^{-4} 	ext{ N}) (1 	ext{ m}) \approx 5.65 	imes 10^{-4} 	ext{ J} \approx 0.56 	ext{ mJ}$
So the answer is closest to 348 J.

A Stone of Volume 1 ×\times× 10-2 M3 Lies at the Bottom of a Freshwater Lake

A Stone of Volume 1 $\times$ 10^-2 M³ Lies at the Bottom of a Freshwater Lake