Question

the resultant of the forces p and q is R if Q is doubled then the resultant also doubles in magnitude . find the angle between p and q​

Answer 1

Answer:

Let take the angle between P and Q is θ.

The force expression according to given conditions are given as,

P

2

+Q

2

+2PQcosθ=R

2

(1)

When Q is doubled,

P

2

+4Q

2

+4PQcosθ=4R

2

(2)

When Q is reversed,

P

2

+Q

2

−2PQcosθ=4R

2

(3)

Subtracting equation (3) from equation (1), we get

4PQcosθ=−3R

2

PQcosθ=

4

−3

R

2

(4)

Substituting the value from equation (4) to equation (1), (2) and (3), we get

P

2

+Q

2

=

2

5

R

2

P

2

+4Q

2

=7R

2

P

2

+Q

2

=

2

5

R

2

Simplify the above equations, we get

P

2

=R

2

Q

2

=

2

3

R

2

Thus, the ratio is P:Q:R=

2

:

3

:

2

.