JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Heat & Thermodynamics

A steel rod of length 1 m and cross sectional area

1 0^{- 4} m^{2}

is heated from

0^{\circ} C

20 0^{\circ} C

without being allowed to extend or bend. The compressive tension produced in the rod is

____

\times 1 0^{4} N

.
(Given Young's modulus of steel

= 2 \times 1 0^{11} Nm^{- 2}

, coefficient of linear expansion

= 1 0^{- 5} K^{- 1}

Answer: 4

Solution

Preventing the heated rod from expanding is equivalent to compressing it by the thermal strain

α Δ T

it would otherwise have gained. The resulting stress is

Y α Δ T = (2 \times 1 0^{11}) (1 0^{- 5}) (200) = 4 \times 1 0^{8} N m^{- 2}

, and the force is this stress times the cross-sectional area,

F = (4 \times 1 0^{8}) (1 0^{- 4}) = 4 \times 1 0^{4} N

. Expressed as a multiple of

1 0^{4} N

, the compressive force in the rod is

4

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Integer answer