#### Question

In problem 10.9, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms? (Specific gravity of mercury = 13.6)

#### Solution

Height of the water column, *h*_{1} = 10 + 15 = 25 cm

Height of the spirit column, *h*_{2} = 12.5 + 15 = 27.5 cm

Density of water, *ρ*_{1} = 1 g cm^{–3}

Density of spirit, *ρ*_{2} = 0.8 g cm^{–3}

Density of mercury = 13.6 g cm^{–3}

Let *h* be the difference between the levels of mercury in the two arms.

The pressure exerted by height *h*, of the mercury column:

= *hρ*g

= *h* × 13.6g … (*i*)

Difference between the pressures exerted by water and spirit:

`=h_1rho_1g - h_1rho_1g`

= g(25 × 1 – 27.5 × 0.8)

= 3g … (*ii*)

Equating equations (*i*) and (*ii*), we get:

13.6 *h*g = 3g

*h* = 0.220588 ≈ 0.221 cm

Hence, the difference between the levels of mercury in the two arms is 0.221 cm.