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Question

(D) The metal sphere is in equilibrium under the action of three forces: tension $\overrightarrow{T}$,horizontal force $\overrightarrow{P}$,and weight

Vedclass · Accepted Answer

$T = P + W$

Vedclass · Answer

(D) The metal sphere is in equilibrium under the action of three forces: tension $\overrightarrow{T}$,horizontal force $\overrightarrow{P}$,and weight $\overrightarrow{W}$.For equilibrium,the vector sum of these forces must be zero: $\overrightarrow{T} + \overrightarrow{P} + \overrightarrow{W} = 0$.Resolving the tension $\overrightarrow{T}$ into rectangular components:Vertical component: $T \cos 	heta = W$ ... $(i)$Horizontal component: $T \sin 	heta = P$ ... $(ii)$Dividing $(ii)$ by $(i)$,we get: $\frac{T \sin 	heta}{T \cos 	heta} = \frac{P}{W} \implies 	an 	heta = \frac{P}{W} \implies P = W 	an 	heta$.Squaring and adding $(i)$ and $(ii)$:$(T \cos 	heta)^2 + (T \sin 	heta)^2 = W^2 + P^2$$T^2 (\cos^2 	heta + \sin^2 	heta) = W^2 + P^2$$T^2 = W^2 + P^2$.Thus,the statement $T = P + W$ is incorrect.

$A$ 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?

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