First slide

Rolling motion

Question

Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping,

Moderate

A

the heavier sphere reaches the bottom first
B

the bigger sphere reaches the bottom first
C

the two spheres reach the bottom together
D

the information given is not sufficient to tell which sphere will reach the bottom first.

Solution

For rolling without slipping down a rough inclined plane, acceleration
$\large a=\frac {gsin\theta}{(1+I_c/mR^2)}$

For a solid sphere,
$\large a=\frac {gsin\theta}{(1+2/5mR^2/mR^2)}=\frac 57sin\theta$

So both spheres will roll with same acceleration. Therefore, from
$\large s=\frac 12at^2$
, we can conclude that option (3) is correct.

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