A rod of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion α/°C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by ∆TK. Young’s modulus, Y, for this metal is
(A) F/Aα ∆T
(B) F/Aα(∆T - 273)
(C) F/(2A α ∆T)
(D) 2F/(A α ∆T)
[JEE Main 2019]
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Young's modulus
y
=
S
t
r
e
s
s
S
t
r
a
i
n
=
F
/
A
(
Δ
ℓ
/
ℓ
)
=
F
A
(
α
Δ
T
)
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