A solid cylinder and a solid sphere having sa | vedclass

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

Question

(D) For a solid sphere,the moment of inertia is $I_{S} = \frac{2}{5} MR^2$. For a solid cylinder,the moment of inertia is $I_{C} = \frac{1}{2} MR^2$.

Vedclass · Accepted Answer

$\frac{14}{15}$

Vedclass · Answer

(D) For a solid sphere,the moment of inertia is $I_{S} = \frac{2}{5} MR^2$. For a solid cylinder,the moment of inertia is $I_{C} = \frac{1}{2} MR^2$. The acceleration of a body rolling down an inclined plane is given by $a = \frac{g \sin 	heta}{1 + \frac{I}{MR^2}}$. Therefore,the ratio of the acceleration of the cylinder '$a_{c}$' to that of the sphere '$a_{s}$' is: $\frac{a_{c}}{a_{s}} = \frac{1 + \frac{I_{S}}{MR^2}}{1 + \frac{I_{C}}{MR^2}} = \frac{1 + \frac{2}{5}}{1 + \frac{1}{2}} = \frac{\frac{7}{5}}{\frac{3}{2}} = \frac{7}{5} 	imes \frac{2}{3} = \frac{14}{15}$.

$A$ solid cylinder and a solid sphere having same mass and same radius roll down on the same inclined plane. The ratio of the acceleration of the cylinder '$a_{c}$' to that of sphere '$a_{s}$' is

Similar Questions

How can a solid sphere and a hollow sphere of the same material and same size be distinguished without weighing them?

Two identical solid cylinders run a race starting from rest at the top of an inclined plane. If one cylinder slides and the other rolls,which of the following statements is true?

$A$ solid cylinder and a solid sphere of same mass and radius roll without slipping on a rough inclined plane. The force of friction is ..........

$A$ solid sphere rolls down without slipping from the top of an inclined plane of height $28 \text{ m}$ and angle of inclination $30^{\circ}$. The velocity of the sphere, when it reaches the bottom of the plane is (Acceleration due to gravity $= 10 \text{ ms}^{-2}$)

$Assertion$ : 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.

Vedclass Test Series

Exam Paper Generator

Online Exam Module