Question

An object hangs from a spring balance.The balance registers 29 N in air, 19 N when this object is immersed in water, and 22 N when the object is immersed in another liquid of unknown density. What is the density of that other liquid?

Answer 1

Answer:

The density of the other liquid = 700 kg/m³

Explanation:

Given that

balance in the air = 29 N

Lets take the mass of the object = m

Volume of the object = V

m g = 29 N  -----------1           ( assuming that bouncy force due to air is zero)

Spring balance in the water :

Bouncy force due to water =  ρ V g

Density of water = 1000 kg/m³

Spring balance = 19 N

19 + ρ V g = m g    

 19 + ρ V g = 29      

   ρ V g =10                                              ----------2

Spring balance in the another liquid :

Bouncy force due to water =  d V g

d=Density of the other liquid

Spring balance = 22 N

22 + d V g = m g            

22 + d V g = 29    

   d V g =7                                ----------3

Form equation 2 and 3

$\dfrac{\rho}{d}=\dfrac{10}{7}$

${d}=\dfrac{7}{10}\times 1000$

d= 700 kg/m³

Therefore the density of the other liquid = 700 kg/m³