Question

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


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Answer 1

Answer:

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)

Explanation:

Answer 2

Answer:

Mate you can see below:-

Explanation:

Let P and Q be the forces

In first case

R^= P 2^ + Q 2 ^ +2PQcos120°

= P 2 ^ + Q 2^ −PQ

In second case

S^ = P 2^ + Q 2^ +2PQcos60°

,= P 2^ + Q 2 ^ +PQ

Since given S= R

S 2 =3 P 2^^

we get P=Q

Hence ratio is 1:1

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