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JEE Advanced 2013 Question Paper 1 with solutions for online practice
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© examsnet.com
Question : 4
Total: 60
The work done on a particle of mass m by a force,
K
[
x
(
x
2
+
y
2
)
3
/
2
i
ˆ
+
y
(
x
2
+
y
2
)
3
/
2
j
ˆ
]
(K being a constant of appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is:
2
K
π
a
K
π
a
K
π
2
a
0
Validate
Solution:
d
w
=
→
F
⋅
d
→
r
=
→
F
⋅
(
d
x
^
i
+
d
y
^
j
)
=
K
∫
x
d
x
(
x
2
+
y
2
)
3
∕
2
+
y
d
y
(
x
2
+
y
2
)
3
∕
2
x
2
+
y
2
=
a
2
w
=
K
a
3
∫
a
0
x
d
x
+
∫
0
a
y
d
y
=
K
a
3
(
−
a
2
2
+
a
2
2
)
=
0
force is in radial direction so work done by this force along given path (circle) is zero
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