Question

The resultant of two forces 3p and 2p is r if first force ia doubled then the resultant is also doubled the angle between the force is

Answer 1

Hey.

Here is the answer.

Resultant, R =√(a^2+b^2+2abcosx)

by triangle law of vector addition.

So, r = √{(3p)^2+(2p)^2+2×3p×2p×cosx}

or, r = √(9p^2+4p^2+12p^2cosx)

or, r = √(13p^2+12p^2cosx)

According to question;

2r = √{(6p)^2+(2p)^2+2×6p×2p×cosx}

or, 2r =√(36p^2+4p^2+24p^2cosx)

or, 2r = √(40p^2+24p^2cosx)

or, 2{√(13p^2+12p^2cosx)}
= √(40p^2+24p^2cosx)

or, 4(13p^2+12p^2cosx) = (40p^2+24p^2cosx)

or, 52p^2 + 48p^2cosx= 40p^2 + 24p^2cosx

or, 12 p^2 = - 24 p^2cosx

or, cosx = - 1/2

or, x = cos^-1(-1/2)

or, x = 120°

So, angle between the forces is 120°.

Thanks.