Question

Two forces of 10n and 6n act upon a body. the direction of forces are unkown. the resultant forces on the body may be...
1. 15n
2. 3n
3.17n
4. 2n

pls answer step wise n reason for considering theta=??...
pls​

Answer 1

Answer:

Correct option

1.) 15 N

Explanation:

given that,

Two forces of 10n and 6n act upon a body.

and also given that,

the direction is unknown so,

ф between the forces also not given,

let the forces be A and B

where,

A = 10 N

B = 6 N

Resultant of the two forces

= √(A² + B² + 2AB cosф)

putting the values,

Resultant force

= √(10² + 6² + 2(10)(6)cosф)

= √(100 + 36 + 120cosф)

= √(136 + 120cosф)

now,

maximum value of cosф = 1

where

ф = 0°

now,

putting the value of ф as 0°

Resultant = √(136 + 120cosф)

= √(136 + 120 × cos0°)

= √(136 + 120 × 1)

= √(136 + 120)

= √256

= 16 N

and

minimum value of cosф = -1

where,

ф = 180°

so,

Resultant = √(136 + 120cos180)

= √(136 + 120 × (-1))

= √(136 - 120)

= √16

= 4 N

now here,

Maximum resultant = 16 N

Minimum resultant = 4 N

now,

in the options,

1.) 15 N

is between the maximum and minimum resultant force

so,

Correct option

1.) 15 N