GATE 2026 MT – Question 47
Iron powder is compacted at room temperature to 75% of its theoretical density. The as-pressed iron compact is sintered in inert-gas atmosphere at 1200 °C to 90% of its theoretical density. Assuming isotropic shrinkage, the linear shrinkage (in percent) undergone by the iron compact during sintering (rounded off to one decimal place) is ________________ %
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Correct answer: 5.8 to 6.1
Explanation
Mass conservation gives $\rho_iV_i=\rho_fV_f$, so $V_f/V_i=0.75/0.90=5/6$. For isotropic shrinkage, $L_f/L_i=(V_f/V_i)^{1/3}=(5/6)^{1/3}=0.941036$.
The linear shrinkage is $100(1-0.941036)=5.8964\%$, which rounds to **5.9%**. The volume shrinkage is a different quantity.