A solid sphere (mass 2M) and a thin hollow sp | vedclass

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

Question

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

Vedclass · Accepted Answer

Solid sphere will reach the bottom first

Vedclass · Answer

(A) The acceleration $a$ of an object rolling down an inclined plane is given by $a = \frac{g \sin 	heta}{1 + \frac{I}{MR^2}}$,where $I$ is the moment of inertia,$M$ is the mass,and $R$ is the radius.For a solid sphere,$I = \frac{2}{5}MR^2$,so $a_{solid} = \frac{g \sin 	heta}{1 + 2/5} = \frac{5}{7}g \sin 	heta$.For a hollow spherical shell,$I = \frac{2}{3}MR^2$,so $a_{hollow} = \frac{g \sin 	heta}{1 + 2/3} = \frac{3}{5}g \sin 	heta$.Since $\frac{5}{7} > \frac{3}{5}$,the acceleration of the solid sphere is greater than that of the hollow spherical shell.Therefore,the solid sphere will reach the bottom first.

$A$ solid sphere (mass $2M$) and a thin hollow spherical shell (mass $M$) both of the same size,roll down an inclined plane,then

Similar Questions

$Assertion$ : The velocity of a body at the bottom of an inclined plane of given height is more when it slides down the plane,compared to when it rolls down the same plane.
$Reason$ : In rolling down,a body acquires both kinetic energy of translation and rotation.

$A$ cylinder is pure rolling up an incline plane. It stops momentarily and then rolls back. The force of friction

An inclined plane makes an angle of $30^{\circ}$ with the horizontal. $A$ solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration ($g=$ acceleration due to gravity,$\sin 30^{\circ}=0.5$).

$A$ solid sphere rolls down two different inclined planes of the same heights but different angles of inclination.
$(a)$ Will it reach the bottom with the same speed in each case?
$(b)$ Will it take longer to roll down one plane than the other?
$(c)$ If so,which one and why?

$A$ uniform solid cylinder of mass $m$ and radius $r$ rolls along an inclined rough plane of inclination $45^{\circ}$. If it starts to roll from rest from the top of the plane,then the linear acceleration of the cylinder axis will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module