A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?

Question

A disk and a sphere of same radius but different masses roll off 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) Sphere (B) Both reach at the same time (C) Depends on their masses (D) Disk

Tardigrade Admin · Accepted Answer

a = (g sinθ/1+ (K2)R2) for disc ; (K2/R2) = (1/2) = 0.5 for sphere ; (K2/R2) = (2/5) = 0.4 a(sphere) > a(disc) ∴ sphere reaches first

Q. A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?

Sphere

Both reach at the same time

Depends on their masses

Disk

$a = \frac{g s i n θ}{1 + \frac{K ^{2}}{R ^{2}}}$
for disc ; $\frac{K ^{2}}{R ^{2}} = \frac{1}{2} = 0.5$
for sphere ; $\frac{K ^{2}}{R ^{2}} = \frac{2}{5} = 0.4$
a(sphere) > a(disc)
$∴$ sphere reaches first

Q. A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?

Sphere

Both reach at the same time

Depends on their masses

Disk

a=1+R2K2​gsinθ​ for disc ; R2K2​=21​=0.5 for sphere ; R2K2​=52​=0.4 a(sphere) > a(disc) ∴ sphere reaches first

$a = \frac{g s i n θ}{1 + \frac{K ^{2}}{R ^{2}}}$
for disc ; $\frac{K ^{2}}{R ^{2}} = \frac{1}{2} = 0.5$
for sphere ; $\frac{K ^{2}}{R ^{2}} = \frac{2}{5} = 0.4$
a(sphere) > a(disc)
$∴$ sphere reaches first