Question

5
1. (a) Two forces P and Q acting at a point have a resultant R. If Pis
doubled, R is doubled and if Q is doubled and reversed in
direction, even then R is doubled. Show that
P:Q: R = 16:12:15
3.3​

Answer 1

Answer:

Here is your answer...

Step-by-step explanation:

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

.

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