Question

An object of density 10gcm with a mass of 60g tied to a string is submerged in a liquid of 0.8gcm,when half of the object is submerged in the liquid,what is the tension on the string

Answer 1

The tension on the string

$$T=mg-F_{\rm buoyant}$$

$$=mg-g\rho_{\rm liquid}V_{\rm immersed}$$

$$=mg-g\rho_{\rm liquid}\frac{m}{2\rho_{\rm body}}=mg\left(1-\frac{\rho_{\rm liquid}}{2\rho_{\rm body}}\right)$$

$$=0.06\:\rm kg\times 9.8\:\rm N/kg\times \left(1-\frac{0.8}{2\times 10}\right)$$

$$=0.56\;\rm N$$