Question

When a force F acts on a particle of mass m, the acceleration of particle becomes a. Now if two forces of magnitude 3F and 4F acts on the particle (both are at an angle of 90° from mass m) simultaneously , then the acceleration of the particle is
(1) a
(2) 2a
(3) 5a
(4) 8a
The answer is 5a but how?

Answer 1

3f and 4f will produce acceleration 3a and 4a respectively. and the resultant of 3a and 4a would be 5a by Pythagoras

Answer 2

according to Newton's 2nd law of motion, body accelerates along net force acted on body.
so, first of all we have to find net force acted on body.

a/c to question,
two forces 3F and 4F act on the body and also both are at an angle 90° from mass m.
so, net force, $F_{net}=\sqrt{(3F)^2+(4F)^2}=5F$

hence, net force, Fnet = 5F.
now use Newton's law, Fnet = ma'
5F = ma'

given, F = ma [when a force F acts on a particle of mass m, the acceleration of particle becomes a]
so, 5ma = ma' => a' = 5a

hence, Acceleration of the body is 5a
so, option (3) is correct.