Question

Two spheres of the same mass are positioned on a 100 meter ramp with at 20 degree incline. Both spheres have a radius or 5 m and mass of 1000 kg (HUGE SPHERES, think Indiana Jones). The difference is how the mass is distributed. One sphere is completely solid with mass equally distributed throughout it. The second mass has all of its mass distributed at the edge of its radius in a thin shell. So, one sphere is solid, the other is hollow. Both masses are released from rest. How long will it take each to roll down the ramp?

Answer 1

Step-by-step explanation:

acceleration of a rolling body down an inclined surface is given by the formula

a = g sinθ / 1 + k² / R² , θ is inclination , k is radius of gyration , R is radius

It will not depend upon mass .

for solid sphere

k , radius of gyration = √(2/5)R

k² / R² = 2/5 = .4

a = g sin20 / (1 + .4 )

= 2.4 m /s²

from s = ut + 1/2 at²

100 = .5 x 2.4 t²

t = 9.13 s

For hollow sphere

k , radius of gyration = √(2/3)R

k² / R² = 2/3 = .67

a = g sin20 / (1 + .67 )

= 2 m /s².

from s = ut + 1/2 at²

100 = .5 x 2 t²

t = 10 s

So time taken are 9.13 and 10 s respectively.