A rectangular block of wood floats in water with two-thirds of its volume immersed. When placed in another liquid, it floats with half of its volume immersed. Calculate the relative density of the liquid

aydultimate

6 years ago

B is the right answer here, the formula given can truly be used to calculate the relative density of a liquid but not when floatation is involved. here is how to go about it;
since the wood float in water, then
upthrust in water equals its weight
U=mg (Principle of floatation)
⅔ × density of water × volume of the wood × g = mg
⅔×1000×V×10=mg.......equa 1
Since the wood also float in the liquid,
Upthrust in the liquid = mg (principle of floatation)
U = mg
½ × density of the liquid × Volume of the object × g = mg
½ × D × V × 10 = mg ...... equa 2
Since both equations equa mg, hence
⅔×1000×V×10=½×D×V×10
D = 4000/3
D = 1333.33
Relative density = D/1000
hence R.D = 1.33
Option B

It is simpler than this, I only go through this long method to make it explanatory

Python891

2 years ago

Wrong answer and working