First slide

Vectors

Question

The resultant of two forces cannot exceed

Moderate

A

average of the forces
B

algebraic sum of the two forces
C

difference of the two forces
D

none

Solution

If α be the angle between the forces $\vec{P}$
and $\vec{Q}$ , then their resultant is given by $\vec{R}$
$\large \[\sqrt {{P^2} + {Q^2} + 2PQ\cos \alpha } = \sqrt {{P^2} + {Q^2} + 2PQ - 2PQ + 2PQ\cos \alpha } \]$
⇒R =
$\large \sqrt {{{(P + Q)}^2} - 2PQ(1 - \cos \alpha )}$
Since (1+cosα) is positive , magnitude of resultant R is less than or equal to
$\large \sqrt {{{(P + Q)}^2}}$
i.e R ≤ (P+Q), equality sign holds good when (1-cosα) = 0 i.e α =0⁰.

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