Question

Two forces of magnitudes f1 , f2 act at a particle , the magnitude of their resultant is R , Newton where 8  R  12 , then: f1=… Newton , f2 =.… Newton given that " f1 < f2

Answer 1

f1 = 2 N and f2 = 10 N

it is given that Two forces of magnitude f1 , f2 act at a particle of their resultant is R Newton where 8 ≤ R ≤ 12.

we know, resultant of two vectors A and B is given by, = √{A² + B² + 2AB cosΦ} , where Φ is angle between A and B.

if cosΦ = 1 , resultant will be maximum i.e., |A| + |B|

and if cosΦ = -1 , resultant will be minimum i.e., |A| - |B|

so, |A| - |B| ≤ (A + B) ≤ |A| + |B|

similarly resultant of f1 and f2 is given by,

f2 - f1 ≤ R ≤ f1 + f2 [ as f1 < f2 ]

on comparing we get,

f2 - f1 = 8 and f1 + f2 = 12

after solving we get, f1 = 2 and f2 = 10

Answer 2

Answer:

resultant of two vectors A and B is given by, = √{A² + B² + 2AB cosΦ} , where Φ is angle between A and B.

if cosΦ = 1 , resultant will be maximum i.e., |A| + |B|

and if cosΦ = -1 , resultant will be minimum i.e., |A| - |B|

so, |A| - |B| ≤ (A + B) ≤ |A| + |B|

similarly resultant of f1 and f2 is given by,

f2 - f1 ≤ R ≤ f1 + f2 [ as f1 < f2 ]

on comparing we get,

f2 - f1 = 8 and f1 + f2 = 12

after solving we get, f1 = 2 and f2 = 10