GATE 2022 MN – Question 63
A 12 m thick coal seam dips 30°, has density 1.41 tonne/m³ and is mined with a 45° pit slope. The limiting instantaneous stripping ratio is 10 m³/tonne. Find the surface pit length L shown, in metres to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 320.00 to 330.00
Explanation
The keyed sectional approximation uses 12 m as the coal intercept along the pit face. An incremental slice then gives W/(12×1.41)=10, so the waste intercept W is 169.2 m. Vertical projection H=W sin 45°=119.6425 m. Surface width is H(cot 45°+cot 30°)=326.8693 m, or 326.87 m. Interpretation note: if 12 m denotes true seam thickness normal to the seam, the oblique pit-face intercept requires a sin 75° correction and gives 338.4 m, outside the official range. The source key therefore uses the stated intercept approximation.