The ratio of the accelerations for a solid sphere (mass ‘m’ and radius ‘R’) rolling down an incline of angle ‘θ’ without slipping and slipping down the incline without rolling is:
Answer & explanation
Correct answer: option 1
For rolling motion without slipping on inclined plane acceleration is given by :
arolling = \(\frac{g sin \theta}{1 + \frac{K^2}{R^2}}\)
for solid sphere, \(\frac{k^2}{R^2}= \frac{2}{5}\)
And for slipping motion on inclined plane :
aslipping = g sin \(\theta\)
Ratio : \(\frac{a_{rolling}}{a_{slipping}} = \frac{5}{7}\)