Question

A symmetrical uniform solid cube of side $5m$ is placed on a horizontal surface beside a vertical wall, one side of cube is making an angle ${45}^{\circ }$ with the floor as shown. If coefficient of friction $\mu$ is the same for both wall and floor, the minimum value of $\mu$ for cube not to slip.

• A. $\mu =1$
• B. $\mu =0$
• C. $\mu =\frac{1}{3}$
• D. Impossible to balance for any value of $\mu$

Answer 1

The correct option is B $\mu =0$

Normal reaction at the point of contact of the cube at the lowest point is vertical and passes through the center of the cube.
At angle ${45}^{\circ }$, $N$ and $Mg$ balance each other, they both pass through centre of mass, so no need of friction to balance it.