From an inclined plane,a ring,a disc,a sphere | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The acceleration $a$ of a body rolling down an inclined plane is given by the formula: $a = \frac{g \sin 	heta}{1 + \frac{I}{MR^2}}$,where $I$ is

Vedclass · Accepted Answer

Solid Sphere

Vedclass · Answer

(C) The acceleration $a$ of a body rolling down an inclined plane is given by the formula: $a = \frac{g \sin 	heta}{1 + \frac{I}{MR^2}}$,where $I$ is the moment of inertia,$M$ is the mass,and $R$ is the radius.For a given inclined plane,$g$ and $	heta$ are constant. Therefore,the acceleration $a$ is inversely proportional to the factor $(1 + \frac{I}{MR^2})$.The body with the smallest value of $\frac{I}{MR^2}$ will have the largest acceleration and will reach the base first.- For a ring: $I = MR^2$,so $\frac{I}{MR^2} = 1$.- For a disc: $I = \frac{1}{2}MR^2$,so $\frac{I}{MR^2} = 0.5$.- For a solid sphere: $I = \frac{2}{5}MR^2$,so $\frac{I}{MR^2} = 0.4$.- For a cylinder: $I = \frac{1}{2}MR^2$,so $\frac{I}{MR^2} = 0.5$.Comparing the values,the solid sphere has the smallest value $(0.4)$.Thus,the solid sphere has the highest acceleration and reaches the base first.

From an inclined plane,a ring,a disc,a sphere,and a cylinder of equal radius are rolled without slipping. Which one reaches the base first?

Similar Questions

Consider a situation in which a ring,a solid cylinder,and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and have identical diameters. The correct statement for this situation is:

$A$ solid sphere is thrown up a rough incline. The sphere rolls up without slipping and eventually comes down rolling without slipping. The direction of rolling friction in upward and downward motion respectively is ............

$A$ cylinder and a ring of same mass $M$ and radius $R$ are placed on the top of a rough inclined plane of inclination $\theta$. Both are released simultaneously from the same height $h$. Choose the correct statement$(s)$ related to the motion of each body.

$A$ ball of radius $11 \ cm$ and mass $8 \ kg$ rolls from rest down a ramp of length $2 \ m$. The ramp is inclined at $35^{\circ}$ to the horizontal. When the ball reaches the bottom,its velocity is .......... $m/s$. $(\sin 35^{\circ} = 0.57)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module