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.


best answer shall be marked brainliest ✌​

Answer 1

Answer:

Let the forces be "A" and "B"

Given :

Greatest resultant = 10N

Least resultant = 6N

Each force is increased by 3N.

To find :

Resultant of new forces when kept at 90°.

Calculation:

So as per the question,

A + B = 10 .....................(i)

A - B = 6 ........................(ii)

Solving (i) and (ii) by elimination :

A = 8N and B = 2N.

Each forces have been increased by 3N.

So A' = 8+ 3 = 11 N

and B' = 2+3 = 5N.

Now , new resultant

= √(11² + 5²)

= √( 121 + 25)

= √ ( 146)

= 12.083 N.

So the answer is 12.083 N.

Answer 2

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",

___________________________

Therefore ,

According to the question,

→ x + y = 10 ......(1)

and

→ x - y = 6 .......(2)

Adding (1) and (2) ,

$\rightarrow \sf{\red{ x \: + y + x - y} = \green{10 + 6} }\\ \\ \rightarrow \sf{ 2x = 16} \\ \\ \rightarrow \sf{\red{x \: = 8 \: N}} \\ \\ \sf{put \: x \: = 8 \: \: in \: (2)} \\ \\ \rightarrow \sf{ 8 - y = 6} \\ \\ \rightarrow \sf{ 8 - 6 = y} \\ \\ \rightarrow \sf{\pink{ y \: = 2 \: N}}$

______________________________

According to the question,

Each force increase by " 3 N" ,

$\rightarrow \: \sf{ x_{1} \: = 8 + 3 = 11 \: N} \\ \\ \sf{ and \: } \\ \\ \rightarrow \: \sf{ y_{1}\: = 2 + 3 = 5 \: N}$

Then the resultant of forces is ,

$\implies \sf{ \red{ \sqrt{ {x_{1}}^{2} + {y_{1}}^{2} }} } \\ \\ \because \sf{x_{1} \: = 11 \: \: \: y_{1} \: = 5 \:} \\ \\ \implies \: \sqrt{ {(11)}^{2} + {(5)}^{2} } \\ \\ \implies \: \sqrt{121 + 25} \\ \\ \implies \: \sqrt{146} \sf{ \: or \: 12.083 \: n}$

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

____________________________