A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle θ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction μmin between the mass and the inclined surface such that the mass does not move is:

Free body diagram is shown in the figure. Pseudo force on the object is 2mg in the downward direction as seen from the rocket frame of reference. Normal force in the direction perpendicular to the inclined plane. N=3mgcos(θ) Maximum frictional force in the direction along the plane, Fr=μminN ∴Fr=3μminmgcos(θ) This should balance the force on the block along the downward direction of plane. 3mgsin(θ)=3μminmgcos(θ) μmin=tan(θ)