First slide

Scalars and Vectors

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?

Moderate

A

$P = W \tan θ$
B

$\vec{T} + \vec{P} + \vec{W} = 0$
C

$T^{2} = P^{2} + W^{2}$
D

$T = P + W$

Solution

As the metal sphere is in equilibrium under the effect of three forces therefore $\vec{T} + \vec{P} + \vec{W} = 0$
From the figure
$\begin{array}{l} T \cos θ = W . . . . . . . (i) \\ T \sin θ = P . . . . . . . . (i i) \end{array}$
From equations (i) and (ii), we get $P = W \tan θ and T^{2} = P^{2} + W^{2}$

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