A hole is drilled in a metal sheet. At 27° C, the diameter of hole is 5 cm. When the sheet is heated to 177° C, the change in the diameter of hole is d × 10-3 cm. The value of d will be if coefficient of linear expansion of the metal is 1.6 × 10-5 / ° C.

Question

A hole is drilled in a metal sheet. At 27° C, the diameter of hole is 5 cm. When the sheet is heated to 177° C, the change in the diameter of hole is d × 10-3 cm. The value of d will be if coefficient of linear expansion of the metal is 1.6 × 10-5 / ° C. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

d 0 at 27° C d 1 at 177° C d 1= d 0(1+α Δ T ) d 1- d 0=5 × 1.6 × 10-5 × 150 cm =12 × 10-3 cm

Q. A hole is drilled in a metal sheet. At 27∘C, the diameter of hole is 5cm. When the sheet is heated to 177∘C, the change in the diameter of hole is d×10−3cm. The value of d will be ___ if coefficient of linear expansion of the metal is 1.6×10−5/∘C.

d0​ at 27∘C&d1​ at 177∘C d1​=d0​(1+αΔT) d1​−d0​=5×1.6×10−5×150cm =12×10−3cm

$d_{0}$ at $2 7^{\circ} C & d_{1}$ at $17 7^{\circ} C$
$d_{1} = d_{0} (1 + α Δ T)$
$d_{1} - d_{0} = 5 \times 1.6 \times 1 0^{- 5} \times 150 c m$
$= 12 \times 1 0^{- 3} c m$