0

A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct?

  1. h=r
  2. h=2R
  3. h=0
  4. no relation between h and R (NEET 2002)

Available solutions indicate option 4, but this directly contradicts the information here since rolling will take up energy and hence reduce the acceleration.

Note: I am not interested in the answer to a homework/exam question. I am interested in the concept of whether an object on a horizontal smooth surface will roll. And while I cannot contact the examiners, I do want to understand the concept correctly.

Starlight
  • 347

1 Answers1

2

There is one horizontal force, $F$, acting on the sphere.
enter image description here
Applying two equal magnitude, $F$, and opposite direction to each other forces, $F_1$ and $F_2$, at the centre of mass $C$ results in a force $F_2$ acting at the centre of mass of the sphere which produces a translational acceleration, $a$ of the centre of mass $(F=m\,a)$, and a couple $F\,h$ which produces an angular acceleration, $\alpha$, about the centre of mass $F\,h= I_{\rm com}\alpha$.

So the linear acceleration is independent of the position the force $F$ is applied, Option $D$, and there will be an angular acceleration of the sphere unless $h=0$.

Farcher
  • 104,498