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JEE Main 17 March 2021 Shift 1 Solved Paper
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© examsnet.com
Question : 1
Total: 90
A triangular plate is shown below. A force
F
=
4
∧
i
−
3
∧
j
is applied at point
P
. The torque at point
P
with respect to point
O
and
Q
are
[17 Mar 2021 Shift 1]
−
15
−
20
√
3
,
15
−
20
√
3
15
+
20
√
3
,
15
−
20
√
3
15
−
20
√
3
,
15
+
20
√
3
−
15
+
20
√
3
,
15
+
20
√
3
Validate
Solution:
Given,
F
=
4
∧
i
−
3
∧
j
Resolving the components of position vector in horizontal and vertical direction.
∴
Horizontal component,
r
x
=
r
cos
θ
=
10
cos
60
∘
[
∵
cos
60
∘
=
1
2
]
=
10
×
1
2
=
5
units
Vertical component,
r
y
=
r
sin
θ
=
10
sin
60
∘
[
∵
sin
60
∘
=
√
3
2
]
=
10
×
√
3
2
=
5
√
3
units
∴
Position vector w.r.t.
O
,
r
O
=
5
∧
i
+
5
√
3
∧
j
and position vector w.r.t. Q,
r
Q
=
−
5
∧
i
+
5
√
3
j
Torque at point
P
w.r.t.
O
,
τ
O
=
r
O
×
F
=
(
5
∧
i
+
5
√
3
∧
j
)
×
(
4
∧
i
−
3
∧
j
)
=
(
−
15
−
20
√
3
)
∧
k
=
(
15
+
20
√
3
)
(
−
∧
k
)
Torque at point
P
w.r.t.
Q
,
τ
Q
=
r
Q
×
F
=
(
4
∧
i
−
3
∧
j
)
×
(
−
5
∧
i
+
5
√
3
∧
j
)
=
(
−
15
+
20
√
3
)
∧
k
=
(
15
−
20
√
3
)
(
−
∧
k
)
© examsnet.com
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