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, ___________ .

विकल्प

• the heavier sphere reaches the bottom first

• the bigger sphere reaches the bottom first

• the two spheres reach the bottom together

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

Answer 1

the two spheres reach the bottom together

 

Acceleration of a sphere on the incline plane is given by

\[a = \frac{g\sin\theta}{1 + \frac{I_{COM}}{m r^2}}\] 

\[ I_{COM}\] for a solid sphere \[= \frac{2}{5}m r^2 \] 

\[So,   a = \frac{g\sin\theta}{1 + \frac{2m r^2}{5m r^2}} = \frac{5}{7}g\sin\theta\]

a is independent of mass and radii; therefore, the two spheres reach the bottom together.