Question

A metal rod of cross-sectional area 3 × 10^-6 m² is suspended vertically from one end has a length 0.4 m at 100°C. Now the rod is cooled upto 0°C, but prevented from contracting by attaching a mass 'm' at the lower end. The value of 'm' is ______.

(Y = 10¹¹ N/m², coefficient of linear expansion = 10^-5/K, g = 10m/s²)

Options

• 30 kg

• 40 kg

• 20 kg

• 10 kg

Answer 1

A metal rod of cross-sectional area 3 × 10^-6 m² is suspended vertically from one end has a length 0.4 m at 100°C. Now the rod is cooled upto 0°C, but prevented from contracting by attaching a mass 'm' at the lower end. The value of 'm' is 30 kg.

Explanation:

`triangle"L"="L"prop triangle"T"="FL"/"AY"`

∴ F = AY ∝ `triangle"T"`

∴ Mg = AY ∝ `triangle"T"`

`M=("AY"prop triangle"T")/g=(3xx10^-6xx10^11xx10^-5xx100)/10=30  "kg"`