Question

Two bodies are in equilibrium when suspended in
water from the arm of a balance. The mass of one
body is 60 g and its density is 12 g cm . If the mass
of the other body is 72 g, its density in g cm is​

Answer 1

Density of other body $\rho_2 = 4.23$ $\frac{gram}{cm^{3}}$     Explanation:

Given that,

Mass of one body$m_{1} = \textrm{60 gram}$

Density of one body $\rho_1 = 12$$\frac{gram}{cm^{3}}$

Mass of other body$m_{2} = \textrm{72 gram}$

Density of other body $\rho_2 =$ ?

Effective gravity  for $g_{eff} = g(1 - \frac{\rho_w}{\rho_s})$

Where,$\rho_w =$ for standard fluid (water)

$\rho_s =$ for solid  

Now, two bodies are in equilibrium then,

$m_{1}g_{eff(1)} = m_{2}g_{eff(2)}$

$60 \times g(1 - \frac{1}{12}) = 72 \times g(1 - \frac{1}{\rho_{2}})$

$60 \times \frac{11}{12} = 72 \times g(1 - \frac{1}{\rho_{2}})$

$\frac{55}{72} = (1 - \frac{1}{\rho_{2}})$

$\frac{1}{\rho_{2}} = (1 - \frac{55}{72})$

$\rho_{2} = \frac{72}{17}$ $\frac{gram}{cm^{3}}$

Density of other body$\rho_2 = 4.23$ $\frac{gram}{cm^{3}}$