Home › JEE Advanced › Physics › Rotational Motion › A **uniform cube** of side $a$ sits on a rough i…
A **uniform cube** of side $a$ sits on a rough incline. As $\theta$ is increased, the cube **topples** before sliding if:
A$\mu < 1/2$
B$\mu > 1$ — toppling at $\theta = 45°$ requires $\mu > 1$
C$\mu = 1/2$
DCube cannot topple on incline
Answer & Solution
Correct answer: B. $\mu > 1$ — toppling at $\theta = 45°$ requires $\mu > 1$
Toppling when CG line crosses the lower edge: $\tan\theta_{\text{topple}} = (a/2)/(a/2) = 1$, so $\theta_{\text{topple}} = 45°$. Sliding when $\tan\theta > \mu$, so $\theta_{\text{slide}} = \arctan \mu$. For toppling first: $\theta_{\text{topple}} < \theta_{\text{slide}}$ ⇒ $1 < \mu$. So a cube on a low-friction surface slides first; only if $\mu > 1$ does it topple before sliding.
Related questions
The branch describing the motion of a rotating rigid body about a fixed axis is rotationalSix washers on a light rod illustrate the moment of inertia of a system of:The more massive an object is, the more of this it has in linear motion:Unlike linear position measured in metres, angular position is measured in units that are:Acceleration caused by the change in direction of tangential velocity is called:Several torques acting about one axis are combined by finding their:The perpendicular distance from the axis to the line of the force is called the:The SI unit of torque is the newton multiplied by the: