8. two forces of magnitude 8N and15N respectively act at a point. If the resultant force is 17 N , the angle between the forces has to be
1) 60 degree
2) 45 degree
3)90 degree
4)30 degree
Q. Two forces of 10N and 16N act upon a body. The direction of the forces are unknown. The resultant force on the body may be
1) 15N
2)3N
3)17N
4)2N
need step by step explanation
Q. the vector OA where O is origin is given by a is equals to two 2^i + 2^j . now it is rotated by 45 degree anticlockwise about O. what will be the new vector?
1) 2√2
2)2^j
3)2^i
4)2√2^i
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Answers
1----- 3.)
2-----2.)
3-----4.)
Answer:
1.The equation to use here is the triangular law of vector addition.
F = a²+b²+2abcosθ
Given a = 8 N
b = 15 N
F = 17 N
we need to find the value of θ
if we put all values in the above equation, we get
17²= 8²+15²+2.8.15.cosθ
289= 64+ 225+ 240cosθ
240cosθ= 0
cosθ= 0
θ= 90°answer
then option(3)
2. The resultant of two vectors A and B should always lie between (A+B) and (A-B)
Thus the resultant should lie between 16N and 4N.
So, the resultant should be any in between these values. I think
15n is your answer
then option(1)
3.Let OA=a
x component is j^
cosθ=a.b/|a| |b|
cosθ=2/2√2
cosθ=1/√2
θ=45°
angle rotated through 45° anti clockwise
then new angle will be 45+45=90°
x component will be zero
y component will be 2√2i^
the new vector is 2√2i^
then option(4)