A disk and a sphere of same radius but different masses roll on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?
A disk and a sphere of same radius but different masses roll on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?
A). Depends on their masses
B). Sphere
C). Disk
D). Both reach at the same time
1 answers
Sphere
The sphere will reach the bottom faster than the disk. It is because the disk has a higher rotational inertia than the solid:
I= mr²
I is the rotational inertia where m is the mass and r is the square of distance from the axis of rotation. in the case of disk I is greater due to r and more the I, more is the rotational K.E. Then for conservation of energy Translational K.E will be less.
mgh= K.E (T) + K.E (R)
so in case of sphere translational K.E will be more, meaning more final velocity and it will reach the bottom faster.
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