Standing waves are generated on a sonometer string loaded with a cylindrical body. If the cylinder is completely immersed in water, the length of the loops changes by a factor of $2.2$ . The specific gravity of the material of the cylinder is
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$f=\frac{V}{\lambda_{1}}=\frac{1}{\lambda_{1}} \sqrt{\frac{T_{1}}{\mu}}$
$\mathrm{f}=\frac{\mathrm{V}}{\lambda_{1}}=\frac{1}{\lambda_{1}} \sqrt{\frac{\mathrm{T}_{2}}{\mu}}$
$\frac{1}{\lambda_{1}} \sqrt{\frac{T_{1}}{\mu}}=\frac{1}{\lambda_{2}} \sqrt{\frac{T_{2}}{\mu}}$
$\sqrt{\frac{\mathrm{T}_{1}}{\mu}}=\left(\frac{\lambda_{1}}{\lambda_{2}}\right) \sqrt{\frac{\mathrm{T}_{2}}{\mu}}$
$\mathrm{T}_{1}=(2.2)^{2} \cdot \mathrm{T}_{2}$
$\mathrm{Mg}=4.84\left[\mathrm{Mg}-\frac{\mathrm{M}}{(\mathrm{S} \cdot \mathrm{G})} \cdot \mathrm{g}\right]$
$1=4.84-\frac{4.84}{\mathrm{S.G}}$
$\frac{4.84}{\mathrm{S.G}}=3.84 \Rightarrow \mathrm{S.G}=\frac{4.84}{3.84}$
$\Rightarrow \mathrm{S.G}=1.26$
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