First slide

Mechanical equilibrium force cases

Question

A metal sphere is hung by a string fixed to a wall. The forces acting on the sphere are shown in figure. Which of the following statements is NOT correct?

Moderate

A

$\vec{N} + \vec{T} + \vec{W} = 0$
B

$T^{2} = N^{2} + W^{2}$
C

$T = N + W$
D

$N = W \tan θ$

Solution

As the body is in equilibrium, so vector sum of all three forces $\vec{N}, \vec{T} and \vec{W}$ should be zero. Hence (a) is correct. Now
$T \sin θ = N - - - - (1)$
$T \cos θ = W - - - - - (2)$
(l)+(2) $\Rightarrow \tan θ = \frac{N}{W}$
$\Rightarrow$ N = W tan $θ$ . Hence (d) is correct.
Squaring and adding (1) and (2); $T^{2} = N^{2} + W^{2}$
Hence (b) is correct.
Hence (c) is incorrect.

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