Question

two forces A and B have resultant R1 ,if B is doubled the resultant R2 is at right angle to A then

a)R1=A

b)R1=B

c)R2=A

d)R2=B

Answer 1

Here x component of A = A 
X component of 2B       = 2BcosФ
X component of Resultant = 0 

I.e. A + 2BcosФ = 0 
cosФ = -A/2B

also R1 = √(A² + B² + 2ABcosФ)
             =√ [A² + B² + 2AB(-A/2B)]
             =√A² + B² -A²
R1 = √B²

R1 = B so , option b ) is correct