Question

if the greatest and lest resultant of 2 forces acting at a point is 10N &6N respectively
if each force is increased by 3N the resultant of new force when acting at 90 degree to each other​

Answer 1

Given:

$\rm F_{greatest} = 10 \: N \\ \rm F_{least} = 6 \: N$

To Find:

Resultant of the two new forces when each force is increased by 3 N and acting at 90° to each other

Answer:

$\rm F_{greatest} =F_1 + F_2 = 10 \: N \: \: ...eq_1 \\ \rm F_{least} = F_1 - F_2 = 6 \: N \: \: ...eq_2$

By adding $\rm eq_1$ & $\rm eq_2$ we get:

$\rm F_1 + F_2 + F_1 - F_2 = 10 + 6 \\ \\ \rm 2F_1 = 16 \\ \\ \rm F_1 = \dfrac{16}{2} \\ \\ \bf F_1 = 8 \: N \\ \\ \\ \rm F_1 + F_2 = 10 \\ \\ \rm F_2 = 10 - F_1 \\ \\ \rm F_2 = 10 - 8 \\ \\ \bf F_2 = 2 \: N$

Now, new force when each force is increased by 3 N:

$\rm F_1' = F_1 + 3 \\ \\ \rm F_1' = 8 + 3 \\ \\ \rm F_1' = 11 \: N \\ \\ \\ \rm F_2' = F_2 + 3 \\ \\ \rm F_2' = 2 + 3 \\ \\ \rm F_1' = 5 \: N$

Resultant of new force:

$\rm \implies R = \sqrt{{F_1'}^{2}+{F_2'}^{2}} \\ \\ \rm \implies R = \sqrt{ {11}^{2} + {5}^{2} } \\ \\ \rm \implies R = \sqrt{121 + 25} \\ \\ \rm \implies R = \sqrt{146} \: N$

$\therefore$ $\boxed{\mathfrak{Resultant \ (R) = \sqrt{146} \ N}}$

Answer 2

Answer:

Question :-

The greatest and least resultant of two forces acting at a point is 10 and 6N ,respectively. If each force is increased by 3N ,find the resultant of new forces when acting at a point at an angle of 90°with each other.

Answer :-

→ Resultant of new forces is 12.083 N or √(146) N

To Find :-

→ Resultant of net forces .

Explanation :-

Given that ,

Greatest resultant force = 10 N

Least resultant force = 6 N

Let , the forces are "x" and "y",

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Therefore ,

According to the question,

→ x + y = 10 ......(1)

and

→ x - y = 6 .......(2)

Adding (1) and (2) ,

$\begin{gathered}arrow \sf{\red{ x \: + y + x - y} = \green{10 + 6} }\\ \\ arrow \sf{ 2x = 16} \\ \\ arrow \sf{\red{x \: = 8 \: N}} \\ \\ \sf{put \: x \: = 8 \: \: in \: (2)} \\ \\ arrow \sf{ 8 - y = 6} \\ \\ arrow \sf{ 8 - 6 = y} \\ \\ arrow \sf{\pink{ y \: = 2 \: N}}</p><p> </p><p>$

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According to the question,

Each force increase by " 3 N" ,

$\begin{gathered} ➡ \sf{ x_{1} \: = 8 + 3 = 11 \: N} \\ \\ \sf{ and \: } \\ \\ \: ➡\sf{ y_{1}\: = 2 + 3 = 5 \: N} \\\end{gathered} </p><p></p><p>$

Then the resultant of forces is ,

$\begin{gathered}\implies \sf{ \red{ \sqrt{ {x_{1}}^{2} + {y_{1}}^{2} }} } \\ \\ \because \sf{x_{1} \: = 11 \: \: \: y_{1} \: = 5 \:} \\ \\ \implies \: \sqrt{ {(11)}^{2} + {(5)}^{2} } \\ \\ \implies \: \sqrt{121 + 25} \\ \\ \implies \: \sqrt{146} \sf{ \: or \: 12.083 \: n} \\ \\\end{gathered} </p><p></p><p>$

Therefore the resultant of new forces is √(146) or 12.083 N.

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