A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an and released,
A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an and released. The friction coefficients betwi objects and the incline are same and not sufficie] allow pure rolling. Least time will be taken in re the bottom by
(a) the solid sphere
(b) the hollow sphere
(c) the disc
(d) all will take same time.
1 Answers
(d) all will take same time.
Explanation:
Since pure rolling does not occur, the objects slide.
Therefore on each of them, a frictional force acts against the motion.
Now, the normal force on each of the objects =mg.cosθ.
Frictional force = µ*mg.cosθ
Net force along the incline = mg.sinθ -µ*mg.cosθ
= m(g.sinθ -µg.cosθ)
Acceleration of each of the block
= m(g.sinθ -µg.cosθ)/m = (g.sinθ -µg.cosθ)
Since the accelerations and the initial velocities are same the time taken to reach the bottom will be the same for all objects.
Time can be calculated as in the previous explanation.