The mechanical quantity, which has dimensions of reciprocal of mass ($M^{-1}$), is:

To determine which quantity has the dimensions of the reciprocal of mass ($M^{-1}$), we analyze the dimensional formulae of the given options:

1. Gravitational Constant ($G$): From the Universal Law of Gravitation, $F = G \frac{m_1 m_2}{r^2}$ . Rearranging for $G$ gives $G = \frac{Fr^2}{m_1 m_2}$. Substituting the dimensions of force ($[MLT^{-2}]$), distance ($[L]$), and mass ($[M]$), we get: $[G] = \frac{[MLT^{-2}][L^2]}{[M^2]} = [M^{-1}L^3T^{-2}]$ . This contains the reciprocal of mass.

2. Angular Momentum ($L$): Defined as the product of moment of inertia and angular velocity, its dimensions are $[ML^2T^{-1}]$ .

3. Torque ($\tau$): Defined as the product of force and the perpendicular distance, its dimensions are $[ML^2T^{-2}]$ .

4. Coefficient of Thermal Conductivity: Its dimensional formula is $[MLT^{-3}K^{-1}]$ .

Therefore, only the gravitational constant has dimensions involving $M^{-1}$.