A Mohr-Coulomb envelop between shear stress, $\tau$ and normal stress, $\sigma_n$ of a sandstone rock is given as

$\tau = 7.5 + 0.84 \sigma_n \quad (\text{unit of stresses is MPa})$

A sandstone sample is tested in triaxial mode with confining pressure of 5.0 MPa. The value of the shear stress, $\tau$ in MPa at the failure, is_____. (round off up to 2 decimals)

The real rate of return from a mining project is 14%. If the inflation rate over the entire life of the mine is 5.5 %, then the nominal rate of return in %, is _____. (round off up to 2 decimals)

In an opencast coal mine, blast vibrations are measured at two locations, A and B simultaneously for a maximum charge per delay (Q) of 1200 kg as given.

Assume the relation

$PPV = K \left( \frac{D}{\sqrt{Q}} \right)^{-\beta}$

where, $K$ and $\beta$ are site constants. The PPV in mm/s, at a distance of 200 m from the blast face, is _____. (round off up to 2 decimals)

A 35.0 kW motor transmits power to a pulley of 600 mm diameter, which rotates at 400 rpm to drive a flat belt. The tension in the tight side is 2.5 times of the slack side. Neglect all transmission losses. If the maximum allowable tension is 8.0 N per mm of belt width, then the minimum width of the belt in mm, is _____. (round off up to 2 decimals)

The spherical semivariogram model $(\gamma(h))$ is represented by the following expression, where $h$ is the lag distance.

The parameters $C_0$, $C$ and $a$ are respectively known as

Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction X, the planar image of the assembly appears as Figure B.

If viewed from direction Y, the planar image of the assembly (Figure A) will appear as

A scanline survey between points A and B of a rock mass is shown. Consider $RQD = 100 \times (0.1\lambda + 1) \times \exp(-0.1\lambda)$, where, $\lambda$ is the frequency of discontinuity per m. The RQD of the rock mass is_____. (round off up to 2 decimals)

The roof convergence data for 30 days at a monitoring station in a coal mine gallery is given.

The management decides on a Trigger Action Response Plan (TARP) if the following two premises occur simultaneously.

Premise 1: Rate of convergence exceeds 1.5 mm/day between two consecutive measurements.

Premise 2: Rate of cumulative increase in convergence exceeds 1.0 mm/day.

Identify the day on which TARP is enforced in that gallery.

A solid ball of mass 10 kg is subjected to forces as shown. The magnitude of the acceleration in m/s², is ______. (round off up to 2 decimals)

A longitudinal section of a mined out stope block in a copper mine is shown by the shaded portion. For a uniform thickness of the stope block, the percentage of ore recovery, is ______. (round off up to 2 decimals)