JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Laws of Motion

Three force

F_{1} = 10 N

F_{2} = 8 N

F_{3} = 6 N

are acting on a particle of mass 5 kg. The forces

F_{2}

and

F_{3}

are applied perpendicular so that particle remains at rest. If the force

F_{1}

is removed, then the acceleration of the particle is:

(A) $2 ms^{- 2}$ ✓ Correct
(B) $0.5 ms^{- 2}$
(C) $4.8 ms^{- 2}$
(D) $7 ms^{- 2}$

Answer: (A)

Solution

Since the particle is initially at rest, the net force is zero. Forces

F_{2}

and

F_{3}

are perpendicular, so their resultant is

F_{2}^{2} + F_{3}^{2} = 64 + 36 = 10

N. This resultant must balance

F_{1} = 10

N (in the opposite direction). When

F_{1}

is removed, the net force on the particle is the resultant of

F_{2}

and

F_{3}

, which is 10 N. Using Newton's second law:

a = \frac{F _{n e t}}{m} = \frac{10}{5} = 2 ms^{- 2}

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Single correct option

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