question_answer

A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong

A)             \[P=W\,\tan \theta \]

B)             \[\overrightarrow{T}+\overrightarrow{P}+\overrightarrow{W}=0\]

C)             \[{{T}^{2}}={{P}^{2}}+{{W}^{2}}\]

D)             \[T=P+W\]

Correct Answer: D

Solution :

                                           As the metal sphere is in equilibrium under the effect of three forces therefore \[\overrightarrow{T}+\overrightarrow{P}+\overrightarrow{W}=0\] From the figure \[T\cos \theta =W\]                                                       ?(i)                           \[T\sin \theta =P\]                                          ?(ii)                    From equation (i) and (ii) we get \[P=W\,\tan \theta \]                     and \[{{T}^{2}}={{P}^{2}}+{{W}^{2}}\]