Question

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. T= P+W
• C. $T^2$ = $P^2$ + $W^2$
• D. none of these

Answer 1

The correct option is B T= P+W

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= Wtan $\theta$
and $T^2$ = $P^2$ + $W^2$