question_answer

A block of mass 20 kg is balanced by three strings A, B and C as shows in figure. Ratio of tensions in strings A and B \[({{T}_{A}}/{{T}_{B}})\]: is

A)              \[\frac{5}{8}\]                       

B)  \[\frac{5\sqrt{3}}{8}\]

C)  \[\frac{5}{6}\]                       

D)  \[\frac{8}{5}\]

Correct Answer: A

Solution :

From the diagram below:                         \[{{T}_{A}}\cos {{\theta }_{1}}={{T}_{B}}\sin {{\theta }_{2}}\]             \[\Rightarrow \]            \[{{T}_{1}}\cos {{37}^{o}}={{T}_{B}}\,\sin {{30}^{o}}\]                         \[{{T}_{A}}\times \frac{4}{5}={{T}_{B}}\times \frac{1}{2}\]                         \[\frac{{{T}_{A}}}{{{T}_{B}}}=\frac{5}{8}\]