question_answer

A solid sphere of density \[\eta (>1)\] times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the  Sphere is/w, then the tension in the string is given by               

A) \[\left( \frac{\eta -1}{\eta } \right)mg\]

B) \[\eta mg\]

C) \[\frac{mg}{\eta -1}\]

D) \[(\eta -1)mg\]

Correct Answer: D

Solution :

[d] \[T+mg={{F}_{b}}\] \[\therefore \,\,T={{F}_{b}}-mg\] \[=V{{\rho }_{w}}g-mg\] \[=\frac{m}{({{\rho }_{w}}/\eta )}{{\rho }_{w}}g-mg\] \[=(\eta -1)mg.\]