First slide

Vectors

Question

The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at $90^{0}$ with the force of smaller magnitude, what are the magnitudes of forces ?

Moderate

A

12, 5
B

14, 4
C

5, 13
D

10, 8

Solution

Let P be the smaller force and Q be the greater force then according to problem
P+Q = 18 -----(i)
R = $\sqrt{P^{2} + Q^{2} + 2 PQcosθ}$ = 12 ----(ii)
$tanϕ = \frac{Qsinθ}{P + Q cosθ} = \tan 90^{0} = \infty$
$∴$ P+Q cos $θ$ = 0 ---(iii)
By solving (i), (ii) and (iii) we will get P = 5, and Q = 13

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App