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Class 11 NEET Physics Motion in a Plane Questions
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© examsnet.com
Question : 19
Total: 74
The positions vector of a particle
→
R
as a function of time is given by
→
R
=
4
s
i
n
(
2
π
t
)
^
i
+
4
cos
(
2
π
t
)
^
j
. Where
R
is in meters,
t
is in seconds and
^
i
and
^
j
denote unit vectors along
x
-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?
[NEET 2015]
Magnitude of the velocity of particle is 8 meter/second.
Path of the particle is a circle of radius 4 meter.
Acceleration vector is along
−
→
R
.
Magnitude of acceleration vector is
v
2
R
where
v
is the velocity of particle.
Validate
Solution:
👈: Video Solution
Here,
→
R
=
4
s
i
n
(
2
π
t
)
^
i
+
4
cos
(
2
π
t
)
^
j
The velocity of the particle is
→
v
=
d
→
R
d
t
=
d
d
t
[
4
s
i
n
(
2
π
t
)
^
i
+
4
cos
(
2
π
t
)
^
j
]
=
8
π
cos
(
2
π
t
)
^
i
−
8
π
s
i
n
(
2
π
t
)
^
j
Its magnitude is
|
→
v
|
=
√
(
8
π
cos
(
2
π
t
)
)
2
+
(
−
8
π
s
i
n
(
2
π
t
)
)
2
=
√
64
π
2
cos
2
(
2
π
t
)
+
64
π
2
s
i
n
2
(
2
π
t
)
=
√
64
π
2
[
cos
2
(
2
π
t
)
+
s
i
n
2
(
2
π
t
)
]
=
√
64
π
2
(
as
s
i
n
2
θ
+
cos
2
θ
=
1
)
=
8
π
m
∕
s
© examsnet.com
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