First slide

Equilibrium of a particle

Question

In the following figure the masses of the blocks A and B are same and each equal to m. The tensions in the strings OA and AB are T₂ and T₁, respectively. The system is in
equilibrium with a constant horizontal force mg on B. Then T₁ is

Moderate

A

$m g$
B

$\sqrt{2} m g$
C

$\sqrt{3} m g$
D

$\sqrt{5} m g$

Solution

Considering free body diagram of block B
$\begin{array}{l} Σ F_{x} = 0; T_{1} \cos θ_{1} = m g . . . . . . . (i) \\ Σ F_{y} = 0; T_{1} \sin θ_{1} = m g . . . . . . . (ii) \end{array}$
By squaring and adding equations
(i) & (ii), we get
$\begin{array}{l} T_{1}^{2} (\sin^{2} θ_{1} + \cos^{2} θ_{1}) = 2 (m g)^{2} \\ ∴ T_{1} = \sqrt{2} m g \end{array}$

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