find the tension in string & normal reaction on mass 'm' if 'm' is in equilibrium
Answers
Answer:
Resolving the forces parallel and perpendicular to rod.
Along the length of rod.
f=mgsin60
o
=
2
3mg
Hence friction force action on rod at support P will be mg/2
(b) for finding tension we can take torque about support P
T(
4
3
l)=mg(
4
l
)orT=
3
mg
(c) Just before cutting the string the rod is at equilibrium. Considering the forces perpendicular to rod length
N+T=mgcos60
o
⇒N=
2
mg
−
3
mg
=
6
mg
(d) Just after cutting the string the equilibrium of the rod will disturbed. The rod will have angular acceleration.
As the rod does not slip point P will be at rest at the time just after cutting the string
We can apply torque equation about τ
P
=I
P
α
(mgcos60
o
)
4
l
=
⎝
⎛
12
ml
2
+m(
4
l
)
2
⎠
⎞
α⇒α=
7l
6g
(e) If we apply torque equation about centre of mass
N.
4
l
=(
12
ml
2
)α
N.
4
l
=(
12
ml
2
)(
7l
6g
)⇒N=
7
2
mg