question_answer

A uniform sphere of weight W and radius 5cm is being held by a string as shown in the figure. The tension in the string will be:                                              [JEE ONLINE 09-04-2013]

A)             \[12\frac{W}{5}\]

B) \[5\frac{W}{12}\]

C)             \[13\frac{W}{12}\]

D) \[13\frac{W}{12}\]

Correct Answer: D

Solution :

[d]

\[T\cos \theta =w\]

\[T=\frac{w}{\cos \theta }\]

\[\cos \theta =\frac{AB}{AC}=\frac{AB}{AD+BC}=\frac{AB}{8+5}=\frac{AB}{13}\]

From right angle triangle \[AB=12\]

So                    \[T=\frac{w\times 13}{12}\]