Question

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 $\theta$ with the horizontal, a point object of mass $m$ is kept. The minimum coefficient of friction ${\mu }_{m}in$ between the mass and the inclined surface such that the mass does not move is:

• A. $3\tan \theta$
• B. $\tan \theta$
• C. $\tan 2\theta$
• D. $2\tan \theta$

Answer 1

Answer: (B)

$\tan \theta$

Free body diagram is shown in the figure.

Psuedo 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.

$N=3mg\cos \left(\theta \right)$

Maximum frictional force in the direction along the plane,

$F_r={\mu }_{m}N$

$\therefore F_r=3{\mu }_{m}mg\cos \left(\theta \right)$

This should balance the force on the block along the downward direction of plane.

$3mg\sin \left(\theta \right)=3{\mu }_{m}mg\cos \left(\theta \right)$

${\mu }_m=\tan \left(\theta \right)$