A solid sphere of mass 2M and a thin hollow s | vedclass

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

Question

(A) The time taken to reach the bottom of an inclined plane is given by $t = \frac{1}{\sin 	heta} \sqrt{\frac{2h}{g} \left( 1 + \frac{K^2}{R^2} igh

Vedclass · Accepted Answer

The solid sphere will reach the bottom first.

Vedclass · Answer

(A) The time taken to reach the bottom of an inclined plane is given by $t = \frac{1}{\sin 	heta} \sqrt{\frac{2h}{g} \left( 1 + \frac{K^2}{R^2} ight)}$.For a solid sphere,the radius of gyration factor is $\frac{K^2}{R^2} = \frac{2}{5} = 0.4$.For a hollow spherical shell,the radius of gyration factor is $\frac{K^2}{R^2} = \frac{2}{3} \approx 0.67$.Since the time $t$ is directly proportional to $\sqrt{1 + \frac{K^2}{R^2}}$,the object with the smaller value of $\frac{K^2}{R^2}$ will take less time to reach the bottom.Because $\left( \frac{K^2}{R^2} ight)_{	ext{solid}} < \left( \frac{K^2}{R^2} ight)_{	ext{hollow}}$,the solid sphere reaches the bottom first.

$A$ solid sphere of mass $2M$ and a thin hollow spherical shell of mass $M$ of the same radius roll down an inclined plane simultaneously. Then,

Similar Questions

$A$ solid cylinder of mass $m$ is wrapped with an inextensible light string and is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is: [The coefficient of static friction,$\mu_{s}$,is $0.4$]

Two discs having masses in the ratio $1:2$ and radii in the ratio $1:8$ roll down without slipping one by one from an inclined plane of height $h$. The ratio of their linear velocities on reaching the ground is ........

$A$ solid cylinder is placed on a rough surface of inclination $\theta$. The minimum value of the coefficient of static friction between the cylinder and the surface so that the cylinder rolls without slipping is:

$A$ solid sphere rolls down without slipping on an inclined plane,then the percentage of rotational kinetic energy of the total energy will be ........ $\%.$

$A$ disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

Vedclass Test Series

Exam Paper Generator

Online Exam Module