A glass cylinder contains `m_0=100g` of mercury at a temperature of `t_0=0^@C`. When temperature becomes `t_1=20^@C` the cylinder contains `m_1=99.7g` of mercury The coefficient of volume expansion of mercury `gamma_(He)=18xx(10^(-5)//^(@)C` Assume that the temperature of the mercury is equal to that of the cylinder. The corfficient of linear expansion of glass `alpha` is

Options

A. `10^(-5)//^(@)C`
B. `2xx10^(-5)//^(@)C`
C. `3xx10^(-5)//^(@)C`
D. `6xx10^(-5)//^(@)C`

Answer

A

Explanation

When the cylinder is heated its volume increases as `V_t=V_0(1+gamma'_(g)t)` ..(i)
If the densities of mercury at the temperatures `t_0` and `t_1` are denoted by `rho_0` and `rho_1`
`m_0=V_0rho_0` and `m_1=V_1rho_1` (ii)
`m_t=m_0`
`rho_t=(rho_0)/((1+gamma_(hg)t))` .(iii)
`gamma_("glass")=(m_t(1+gamma_(Hg)t_t)-m_0)/(m_0t_0)`
`=(99.7(1+18xx10^-5xx20)-100)/(100xx20)`
`=2.946xx10^(-5)//^(@)C`
The coefficient of linear expansion of glass
`alpha_("glass")=(gamma_("glass"))/(3) = 10^(-5)//^(@)C`