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JEE Advanced 2021 Paper 2
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Section:
Physics
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© examsnet.com
Question : 1
Total: 57
One end of a horizontal uniform beam of weight
W
and length
L
is hinged on a vertical wall at point
O
and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point
Q
, at a height
L
above the hinge at point
O
. A block of weight
α
W
is attached at the point
P
of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of
(
2
√
2
)
W
. Which of the following statement(s) is(are) correct?
[JEE Adv 2021 P2]
The vertical component of reaction force at
O
does not depend on
α
The horizontal component of reaction force at
O
is equal to
W
for
α
=
0.5
The tension in the rope is
2
W
for
α
=
0.5
The rope breaks if
α
>
1.5
Validate
Solution:
Since
O
Q
=
O
P
∴
∠
P
=
∠
Q
=
45
∘
At equilibrium
R
y
+
T
√
2
=
W
+
α
W
.....(1)
and
R
x
=
T
√
2
.....(2)
Torque about point '
O
'
W
L
2
+
α
W
L
=
T
√
2
L
∴
T
=
√
2
(
W
2
+
α
W
)
.....(iii)
∴
R
x
=
T
√
2
=
(
W
2
+
α
W
)
Therefore for
α
=
0.5
R
x
=
W
2
+
α
W
=
W
2
+
0.5
W
or
R
x
=
W
i.e., the horizontal component of reaction force at, 0 ,
R
x
=
W
for
α
=
0.5
Now torque about point
P
T
y
L
=
W
L
2
⇒
R
y
=
W
2
The vertical component of reaction force at
O
does not depend on
α
As per question, rope can sustain a maximum tension of
2
√
2
W
∴
2
√
2
W
=
√
2
(
W
2
+
α
W
)
⇒
2
=
1
2
+
α
∴
α
=
3
2
© examsnet.com
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