G. Two particles A and B move on coplanar concentric circles of radii 1m and 2m with angular velocities Irad/s and 0.5rad/s (in the same sense) respectively. At 0=- T radian, relative angular velocity between n B and A is zero. Find the value of n
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Answer:
The correct option is C
ω
(
R
2
−
R
1
)
^
i
Both
A
and
B
are moving on the circular path with same angular speed
(
ω
)
∴
Angular displacement of both particles in interval of
Δ
t
=
π
2
ω
s
is:
θ
=
ω
×
Δ
t
=
ω
×
π
2
ω
=
π
2
rad
Both particles have their angular displacement in opposite directions.
∴
Position of particles at
t
=
π
2
ω
s
is as shown in figure:
Velocities of particles at
t
=
π
2
ω
s
are:
−→
v
A
=
−
ω
R
1
^
i
−→
v
B
=
−
ω
R
2
^
i
The relative velocity is given by:
→
v
A
B
=
(
→
v
A
−
→
v
B
)
=
−
ω
R
1
^
i
−
(
−
ω
R
2
^
i
)
∴
→
v
A
B
=
ω
(
R
2
−
R
1
)
^
i
Verified answer
The amount of n is n_B = 0.5.
Given,
I R = 0.5m
R1 = 1m
R2 = 2m
To find,
Value of n at 0 = -1
Solution,
The relative angular velocity between particles A and B is the difference between their angular velocities. At t = 0, the relative angular velocity between A & B is 0.5 rad/s - 1 rad/s = -0.5 rad/s.
The relative angular velocity between A & B is given by the following equation:
ω_rel = ω_B - ω_A = n_B - n_A
Substituting the given values, we have:
-0.5 rad/s = n_B - 1
Solving for n_B, we find that n_B = 0.5.
Therefore, the amount of n is n_B = 0.5
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