979 Views

The resultant of two forces P and Q is R. If Q is double the new resultant becomes perpendicular to P. Prove that P =R by triangle law.


Azhar aftab 29th Mar, 2019
Answer (1)
Debosmitha Bhattacharyya Student Expert 29th Mar, 2019

Hello Azhar,

Resultant of two forces P and Q is R


R = P + Q


|R| = sqrt(P^2 + Q^2 + 2PQCosθ)


When Q is doubled new resultant R’ is


R’ = P + 2Q


Since it is perpendicular to P, the dot product of R’ and P is zero


(R’).(P) = 0


(P + 2Q).(P) = 0


P^2 + 2PQCosθ = 0


(Dot product of P and P is P^2 and that of P and 2Q is 2PQCosθ)


Cosθ = -P/(2Q)


R = sqrt(P^2 + Q^2 + 2PQCosθ)


R = sqrt(P^2 + Q^2 + 2PQ*(-P/(2Q))


R = sqrt(P^2 + Q^2 - P^2)


R = Q

Hope this helps.

Related Questions

Amity University | LLM Admiss...
Apply
Ranked as India’s #1 Not for profit pvt. University by India Today.
Amity University, Noida Law A...
Apply
700+ Campus placements at top national and global law firms, corporates and judiciaries
Graphic Era (Deemed to be Uni...
Apply
NAAC A+ Grade | Among top 100 universities of India (NIRF 2024) | 40 crore+ scholarships distributed
Sharda University Admissions ...
Apply
North India's Largest Educational Group | NIRF Ranked 86 | NAAC A+ Grade | Highest Package 1.6 Cr | Applications Closing on 31st July
UPES Integrated LLB Admission...
Apply
Ranked #28 amongst Institutions in India by NIRF | Ranked #1 in India for Academic Reputation by QS Rankings | 16.6 LPA Highest CTC | Last Date to...
Sanskaram University LLM Admi...
Apply
100+ Industry collaborations | 10+ Years of legacy
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books