0

Guest

Courses New

For two equal non parallel forces acting a a point the square of resultant is 3 times the product of forces, what is angle between forces

For two equal non parallel forces acting a a point the square of resultant is 3 times the product of forces, what is angle between forces

Grade:11

2 Answers

Arun
25750 Points
6 years ago

Given two forces P and Q, such that | P | = P, | Q | = Q, and P = Q, acting at a point, such that square of magnitude R of resultant R of P and Q is 3 P² = 3 Q². We are required to find the angle between P and Q.

Let the angle between P and Q is ∅. Then by parallelogram law of vectors we have for the resultant, that,

R² = P² + Q² + 2 P Q Cos ∅ = P² + P² + 2 P P Cos ∅= 2 P² + 2 P² Cos ∅. ……..(1)

We are given that R² = 3 P². Substituting for R² in equation 1, we get,

3 P² = 2 P² + 2 P² Cos ∅, or Cos ∅ = ½ or ∅ = 60° .

The angle between the two forces is 60° 

Shailendra Kumar Sharma
188 Points
6 years ago
Assume the Force be A, B and resultant be C
Given C2=A2+B2+2ABCOS(THETA)
GIVEN A=B
SO C2=2A2+2A2COS(THETA)
NOW C2=3A2
SO 3A2=2A2+2A2COS(tHETA)
S Cos(theta)=1/2
SO ANGLE WILL BE 60 DEGREE

Think You Can Provide A Better Answer ?

Other Related Questions on Vectors

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More