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

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

D) \[T=P+W\]

Correct Answer: D

Solution :

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