Question

the resultant of the two forces p and q is r. if q is doubled the new resultant is perpendicular to p then
a. p=q
b. q=r
3. q= 2r
4. none of these​

Answer 1

Answer:

Option B ; i.e Q=R

Explanation:

Consider that Θ is the angle between P and Q having R resultant

Then we can say that;

R^2=P^2+Q^2+2PQcosΘ......a

When Q is doubled then let the resultant vector be R’

R’^2 = P^2+4Q^2+4PQcosΘ......b

As given in question statement,  R’ is perpendicular to P

4Q^2=P^2+R’^2......c

Merging b and c

R’^2=P^2+P^2+R’^2+4PQcosΘ

2PQcosΘ = −P^2......d

Merging a and d we get

R^2=P^2+Q^2−P^2

Hence R=Q