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A small sphere is hung by a string fixed to a wall as shown in the figure. The sphere is pushed from the wall by a stick. The forces acting on the sphere are as shown. Then, identify the incorrect expression.
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The correct answer is:
$T=P+W$
$\begin{aligned} & \text { i.e., } \Sigma F_x=0 \\ & \Rightarrow \quad P-T \sin \theta=0\end{aligned}$
$P=T \sin \theta$ ...(i)
and $\quad \Sigma F_y=0$
$\Rightarrow \quad W-T \cos \theta=0$
$W=T \cos \theta$ ...(ii)
By dividing Eq. (i) by Eq. (ii), we get
$\frac{P}{W}=\frac{T \sin \theta}{T \cos \theta}$
$\Rightarrow \quad P=W \tan \theta$
and their vector sum is also zero.
i.e. $\quad \mathbf{T}+\mathbf{P}+\mathbf{W}=0$
Resultant of $P$ and $W$ is also equal and opposite to tension $T$
$\therefore \quad T^2=P^2+w^2$
That's why, equation $T=P+W$ is the only incorrect expression.
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