77. A rod of length 2 m starts to roll on a horizontal
surface as shown in figure. At the same time an ant
starts moving from one end (A) of the rod to other
and when the rod rolls through a distance 10 m the
ant reaches the other end (B). Calculate the distance
and displacement of the ant
(a) with respect to the rod.
(b) with respect to the ground.
2 m
B
0
A
10 m
0 1
A
ED
B
Answers
Answered by
2
Answer:
Explanation:
R.E.F image
Let us take the point of reference
as C which is the center of the
(rod & point mass) system
By linear momentum conservation,
mv=3mvcm
vcm=
3
v
I
C
= I (of rod about O) +2m(l/6)
2
+I (Point mass about C
=
12
2ml
2
+
36
2ml
2
+m(
6
2l
)
2
=
6
ml
2
+
18
ml
2
+
9
ml
2
=
3
ml
2
By angular momentum conservation about C,
mv
3
l
=Icw⇒mv
3
l
=
3
ml
2
w
∴
w=
l
v
→ ans.
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