Question

Two forces 10N and 15N are acting on a body. What can be the maximum and minimum resultant
force on the body?
(A)25N and 5N
(B)5N and 25N
(C) 25N and 10N
(D) 10N and 25N
​

Answer 1

Step-by-step explanation:

two force = 10n & 15n

max => if then two force acts on the same side !!

Fnet = 10+15 = 25n

min => if the forces are acting opposite to each other!!

Fnet = 15-10 = 5n

therefore, 25n is the max , 5n is the min !!(A)

Answer 2

The correct option to this question which gives the maximum and minimum resultant force is option A: 25N and 5N.

Given:

Force F1 = 15 N

Force F2 = 10 N

To find:

Maximum resultant force or Fr(max)=?

Minimum resultant force or Fr(min)=?

Solution:

Force is the vector quantity therefore magnitude and direction both are to be considered for calculating the resulting force.

If F1 and F2 are two forces in different direction, forming angle θ then the resultant can be calculated from the following formula:

Resultant force Fr = $\sqrt{F1^{2} + F^{2} + 2F1F2.Cos theta$

Fr(max) =  $\sqrt{F1^{2} + F^{2} + 2F1F2.Cos theta$                (Cos θ = 1)

Fr(max) =  $\sqrt{(F1 + F2)^{2} }$

Fr (max) = F1 + F2

Fr(max) = 10 N + 15 N

Fr(max) = 25 N

In the same way,

Fr(min)  =  $\sqrt{(F1 - F2)^{2}}$                                          (∵Cos θ = -1)

Fr(min)  = F1 - F2

Fr(min)  = 15 N - 10 N

Fr(min)  = 5 N

Hence, the maximum and minimum resultant force is 25N and 5N respectively.

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