Question

Two forces of unequal magnitude
simultaneously act on a particle making an angle Of=120°)
with each other. If one of them is reversed, the acceleration
of the particle is becomes √3 times. Calculate the ratio of
the magnitude of the forces.
​

Answer 1

Let f and F are two unequal forces applied on a particle as shown in figure.

Let a is initial acceleration of particle.

so, F - fcos60° = ma

or, F - f/2 = ma ......(1)

here m is mass of block.

when one of them is reversed. Let f is reversed. then, acceleration becomes √3 times.

i.e., Fnet = m(√3a)

F + fcos60° = √3ma

or, F + f/2 = √3ma .....(2)

from equations (1) and (2),

2F = (1 + √3)ma

F = (1 + √3)ma/2

and f = 2(√3ma - F) = 2√3ma - 2F

= 2√3ma - ma - √3ma

= (√3 - 1)ma

now ratio of f and F = 2(√3 - 1) : (1 + √3)