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: C

Solution :

[c]
As the metal sphere is in equilibrium under the effect of the 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 \[{{T}^{2}}={{P}^{2}}+{{W}^{2}}\]