Question

$\huge\mathbb\green{QUESTION \: !!!!}$
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Answer 1

If two forces are F1 and F2 then

➡️ F1 + F2 = 10N

F1 - F2 = 6N

➡️ Add above two equations

2F1 = 16

F1 = 8N

➡️ From first equation

F2 = 10 - 8 = 2N

➡️ When increased by 3N

F1 = 8N + 3N = 11N

F2 = 2N + 3N = 5N

➡️ Resultant = sqrt(11^2 + 5^2) = sqrt(121 + 25) = sqrt(146)

by solving this u will get approx 11 nd might be 12

Answer 2

Solution:

Let the two forces be:

$\implies$ $\sf{F_{1}}$

$\implies$ $\sf{F_{2}}$

So we have:

$\implies$ $\sf{F_{1} + F_{2}= 10N}$

$\implies$ $\sf{F_{1} - F_{2} = 6N}$

By adding the above two equations,

We get:

$\sf{2F_{1} = 16,\:F_{1} = 8N}$

Now:

$\sf{F_{1} + F_{2} = 10N}$

$\implies$ $\sf{8N + F_{2} = 10N}$

$\implies$ $\sf{F_{2} = 10N - 8N}$

$\implies$ $\sf{F_{2} = 2N}$

When it is increased by 3N:

$\implies$ $\sf{F_{1} = 8N + 3N = 11N}$

$\implies$ $\sf{F_{2} = 2N + 3N = 5N}$

Resultant of new forces:

$\implies$ $\sf{ \sqrt{( {11}^{2} + {5}^{2}) }}$

$\implies$ $\sf{ \sqrt{(121 + 25)}}$

$\implies$ $\sf{ \sqrt{146}}$

Therefore:

Correct option: (1) $\sf{\sqrt{146}N}$