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Question

Find the resultant of three vectors OA,OBandOC shown in figure. Radius of circle is 'R'.
207385_15ef11ebca0744bd8b79bb15eec82ac4.png

A
R(1+2)
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B
R(1+3)
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C
R(2+3)
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D
R(1+5)
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Solution

The correct option is A R(1+2)
Step 1: Resolving Vector
Resolve vector OB in x and y direction.
[Ref. Fig. 2]

Magnitude of vector OA,OB and OC are same.

|OA|=|OB|=|OC|=R

In x direction Rx=OA+OBcos45o
Rx=R+R2

In y direction Ry=OC+OBsin45o
Ry=R+R2

Step 2: Find resultant

Resultant =R2x+R2y+2RxRycos90o

= [R(1+12)]2+[R(1+12)]2

=R(1+12)2

Resultant =R(2+1)
Hence option A is correct

2110327_207385_ans_a305a7e5b0f64bd88cb0c236c468cc10.png

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