Question

A solid sphere rolls down two different inclined planes of same height, but of different inclinations. Consider rolling without slipping. Then, in both cases:

• A. Translational speed and time of descent will be same
  
• B. Translational speed will be same, but time of descent will be different
  
• C. Translational speed will be different, but time of descent will be same
  
• D. Translational speed and time of descent are different
  

Answer 1

The correct option is B Translational speed will be same, but time of descent will be different


In case of pure rolling, mechanical energy remains conserved.
Height of inclined planes are equal,
$\therefore \text{Loss in PE}=\text{Gain in}{KE}_{Rot}+\text{Gain in}{KE}_{Trans}$
Since sphere is starting from rest ${\omega }_i=0,v_i=0$
$\Rightarrow$Translational velocity of sphere will be same while descent, in both the cases.
Now, acceleration of sphere down the inclined plane:
$a\propto \sin \theta$
$s=ut+\frac{1}{2}a{t}^2,u=0$
$\therefore$ Time of descent will be different in both cases.