A solid sphere,a disc,and a solid cylinder,al | vedclass

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

Question

(C) The time taken for an object to roll down an inclined plane is given by $t = \sqrt{\frac{2h}{g \sin^2 	heta} (1 + \frac{K^2}{R^2})}$.For a solid

Vedclass · Accepted Answer

The solid sphere reaches the bottom first.

Vedclass · Answer

(C) The time taken for an object to roll down an inclined plane is given by $t = \sqrt{\frac{2h}{g \sin^2 	heta} (1 + \frac{K^2}{R^2})}$.For a solid sphere,the moment of inertia $I = \frac{2}{5}MR^2$,so $\frac{K^2}{R^2} = \frac{2}{5} = 0.4$.For a disc and a solid cylinder,the moment of inertia $I = \frac{1}{2}MR^2$,so $\frac{K^2}{R^2} = \frac{1}{2} = 0.5$.Since the time $t$ is directly proportional to $\sqrt{1 + \frac{K^2}{R^2}}$,the object with the smallest value of $\frac{K^2}{R^2}$ will reach the bottom first.Comparing the values,$0.4 < 0.5$,therefore the solid sphere reaches the bottom first.

$A$ solid sphere,a disc,and a solid cylinder,all of the same mass and made of the same material,are allowed to roll down from rest on an inclined plane. Then,which of the following is true?

Similar Questions

$A$ solid uniform sphere having a mass $M$,radius $R$ and moment of inertia of $\frac{2}{5} M R^2$ rolls down a plane inclined at an angle $\theta$ to the horizontal starting from rest. The coefficient of static friction between the sphere and the plane is $\mu_s$. Then,

$A$ solid sphere having mass $m$ and radius $r$ rolls down an inclined plane. Then its kinetic energy is

$A$ spherical shell and a solid cylinder of the same radius roll down an inclined plane. The ratio of their accelerations is ..........

$A$ body slides down a smooth inclined plane of inclination $\theta$ and reaches the bottom with velocity $V$. If the same body is a ring which rolls down the same inclined plane, then the linear velocity at the bottom of the plane is:

$A$ solid cylinder is released from rest from the top of an inclined plane of inclination $30^{\circ}$ and length $60 \,cm$. If the cylinder rolls without slipping, then the speed when it reaches the bottom is (in $\,m/s$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module