A uniform rod of mass m is held horizontal by means of two vertical
strings at each end as shown in the figure. If the right string is cut, then
tension in the left string immediately after the cut is ?
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Answers
Answer:
Just after cutting the string the tension of right string will disappear and tension in left string will change. let us draw free body diagram of rod immediately after the string breaks.
Let a
x
and b
y
be the linear accelerations of COM and α the
angular acceleration of the rod about COM as shown.
As no force in horizontal direction. Then ∑F
x
= 0
∴ a
x
= 0 ......(i)
a
y
=
m
∑F
y
=
m
mg−T
....(ii)
Applying torque equation about centre of mass
τ = I
cm
α
T.(Lcos30
0
) =
12
m(2L)
2
.α
⇒ α =
I
τ
=
12
m(2L)
2
TLcos30
0
=
2mL
3
3T
(II)
Now after the string breaks, acceleration of point A in the vertical direction should be zero.
i.e.,
a
y
= Lαcos30
0
(iv)
Solving equations (i),(ii),(iii)and(iv)
T =
11
2mg
and
a =
11
3
3
L
g