1.
Two vectors of qual magnitude. A with angle e between them. The magnitude of the resultant
a) 2A.cos
b) 2A :
2A tan
d) 2A
2.
B
R
IR makes an angle a with A then (@ is the angle
two vector are such that A
between A-B)
b sin
a) na
beoseb)
acos
bacos
ba cose
3.
The resultand of A and is makes an angle a wuh A and with then 11
a) a > A<B b) a < A B ) a = Bü A=B d) all the above
Two forces of magnitudes equal to 2p and prespectively act on a particle. If the first is doubled
and second increased by 12N, the direction of the resukant is unallerted. Then p T 1
a) 6N
b) 45N
€) 24N
d) 12N
Two forces whose magnitudes are in the ratio u 3 : 5 gives a resultant of 35N. If the angle of
inclination be 60°, the magnitude of each force is
a) 3N, 5N
b) KN, ION
c) 9N, 15N
d) 15N, 25N
fiso equal vectors have magnitudes A The magnitude of resultant when angle between them is
a) 2
b)
A
c)2A
d) 3A
Aparticle is perfonning uniform circular motion with a speed of 52 ms. The change in velocity
of the particle when the angle between initial and final positions is 90° is
a) 2 m/s b) 10 ms c) 10 m/s
d) 0
8.
a) 90°
e) 150°
9.
The resultant of two vectors A and B is perpendicular to A and equal to half of the magnitude
of B. The angle between A and B is
11
b) 120°
d) 180°
The maximum value of magnitude of (A-B) is
a) A-B
b)A+B
C) A+B2 d) A - B
The minimum number of non-coplanar forces that can keep a particular in equilibrium is
a)
b)
26 )
3d) 4
10.
Answers
Answered by
0
Answer:
We have,
Two vectors having equal magnitude makes an ∠θ
Let the magnitude of each vector be A is:
R=
(A
2
+A
2
+2A×Acosθ)
=
[2A
2
(1+cosθ)]
2A
2
×2cos
2
θ
=2Acos
2
θ
Now,
Direction :
Let angle between any one of vectors and thne resulatant be θ
tanθ=
Acosθ+A
Asinθ
=
1+cosθ
Sinθ
=
2cos
2
2
θ
2sin
2
θ
.cos
2
θ
By using, sinθ=2sin
2
θ
cos
2
θ
and 1+cosθ=2cos
2
2
θ
=tan
2
θ
It means that, tanθ
′
=tan
2
θ
θ=
2
θ
Explanation:
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