question_answer

A hollow sphere of mass \[M=50kg\]and radius\[r={{\left( \frac{3}{40\pi } \right)}^{1/3}}\]m is immersed in a tank of water (density \[{{\rho }_{w}}={{10}^{3}}kg/{{m}^{3}}\]). The sphere is tied to the bottom of a tank by two wires A and B as shown. Tension in wire A is\[(g=10m/{{s}^{2}})\]            

A) \[125\sqrt{2}N\]

B) \[125N\]

C) \[250\sqrt{2}N\]

D) \[250N\]

Correct Answer: C

Solution :

[c] \[{{T}_{1}}={{T}_{2,}}\,Mg+\sqrt{2}{{T}_{1}}\] \[=\frac{4}{3}\pi {{r}^{3}}{{\rho }_{w}}g\,\,{{T}_{1}}\] \[=250\sqrt{2}N\]