A sphere of mass m and radius R is kept on a rough horizontal surface and pulled with a horizontal force F = αt where α is a constant and t is time. The coefficient of static friction is μs and coefficient of kinetic friction is μk. Which of the following graph correctly shows the variation of acceleration of sphere with time ?

Question

G1 Physics · Accepted Answer

Write translation ΣF=Ma and rotation Στ about CM=I about CMα, together with the no-slip relation v of CM=ωR and a of CM=αR whenever pure rolling applies. Solving the equations for the shown geometry gives Image 3.