Question

Left arm has area 10.0 cm2, right has area 5.00 cm2. 100 g of water isadded to right side. a) Determine the length of the water column. b)density of mercury is 13.6 g/cm3, what distance h does the mercury rise onthe left

Answer 1

Answer:

0.49  cm

Explanation:

We are given that

$A_1=10 cm^2$

$A_2=5 cm^2$

Mass of water,m=100 g

a.$\rho_w=1 g/cm^3$

Volume,$V=\frac{mass}{density}=\frac{100}{1}=100 cm^3$

Length of water column in the right arm=$L=\frac{V}{A_2}=\frac{100}{5}=20 cm$

b.$\rho_m=13.6 g/cm^3$

In equilibrium condition  

Pressure at point A=Pressure at point B

$P+\rho_mg(h+h_2)=P+\rho_wgL$

$hA_1=h_2A_2$

$h_2=\frac{hA_1}{A_2}$

$13.6\times 9.8(h+h(\frac{A_1}{A_2}))=1\times 9.8\times 20$

$13.6\times h(\frac{A_2+A_1}{A_2})=20$

$h=\frac{20A_2}{13.6(A_2+A_1)}$

$h=\frac{20\times 5}{13.6\times (10+5)}=0.49 cm$