JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Laws of Motion

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For a free body diagram shown in the figure, the four forces are applied in the ' x ' and ' y ' directions. What additional force must be applied and at what angle with positive x -axis so that the net acceleration of body is zero?

(A) $2 N, 4 5^{\circ}$ ✓ Correct
(B) $2 N, 13 5^{\circ}$
(C) $\frac{2}{3} N, 3 0^{\circ}$
(D) $2 N, 4 5^{\circ}$

Answer: (A)

Solution

For zero net acceleration, the sum of all forces must be zero. Let the additional force be

F

.

From the figure, the net force from the four given forces is:

F_{net} = (5 - 6) \hat{i} + (7 - 8) \hat{j} = - \hat{i} - \hat{j}

For equilibrium:

F + (- \hat{i} - \hat{j}) = 0 ⟹ F = \hat{i} + \hat{j}

Magnitude:

∣ F ∣ = 1^{2} + 1^{2} = 2 N

Angle with positive x-axis:

θ = tan^{- 1} (\frac{1}{1}) = 4 5^{\circ}

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Single correct option

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