A uniform solid cylinder of radius R and height H is placed upright on a rough horizontal platform of a truck. The truck starts accelerating horizontally with an acceleration a . Assuming the coeffici

Question

A uniform solid cylinder of radius R and height H is placed upright on a rough horizontal platform of a truck. The truck starts accelerating horizontally with an acceleration a . Assuming the coefficient of static friction is large enough to prevent sliding, what is the maximum acceleration a ma x ​ of the truck for which the cylinder does not topple?

TestHub · Accepted Answer

For the cylinder to just topple, the line of action of the resultant of the weight ( $M g$ ) and the pseudo force ( $M a$ ) must pass through the edge about which it topples. The pseudo force acts at the center of mass, which is at height $H /2$ .

Taking torques about the edge of the base (point of rotation), the torque due to the pseudo force tends to topple the cylinder, while the torque due to weight tends to restore it. Condition for just toppling: $M a_{ma x} (\frac{H}{2}) = M g (R)$ . Solving for $a_{ma x}$ : $a_{ma x} = g \frac{2 R}{H}$ .

Physics - Rotation Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main 2028 (Class 11)