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) The velocity $V$ of a body rolling down an inclined plane of height $H$ without slipping is given by the formula: $V = \sqrt{\frac{2gH}{1 + k^2/R^

Vedclass · Accepted Answer

$\sqrt{\frac{14}{15}}$

Vedclass · Answer

(D) The velocity $V$ of a body rolling down an inclined plane of height $H$ without slipping is given by the formula: $V = \sqrt{\frac{2gH}{1 + k^2/R^2}}$,where $k$ is the radius of gyration.For a solid cylinder,the moment of inertia $I = \frac{1}{2}MR^2$,so $k^2/R^2 = 1/2$.For a solid sphere,the moment of inertia $I = \frac{2}{5}MR^2$,so $k^2/R^2 = 2/5$.The ratio of velocities is given by: $\frac{V_{	ext{cylinder}}}{V_{	ext{sphere}}} = \sqrt{\frac{1 + k_{	ext{sphere}}^2/R^2}{1 + k_{	ext{cylinder}}^2/R^2}}$.Substituting the values: $\frac{V_{	ext{cylinder}}}{V_{	ext{sphere}}} = \sqrt{\frac{1 + 2/5}{1 + 1/2}} = \sqrt{\frac{7/5}{3/2}} = \sqrt{\frac{7}{5} 	imes \frac{2}{3}} = \sqrt{\frac{14}{15}}$.

$A$ solid cylinder and a solid sphere,having same mass $M$ and radius $R$,roll down the same inclined plane from the top without slipping. They start from rest. The ratio of the velocity of the solid cylinder to that of the solid sphere,with which they reach the ground,will be:

Similar Questions

$A$ cylinder of mass $M$ and radius $R$ rolls on an inclined plane. The gain in kinetic energy is

Two solid spheres of different mass,radii,and density roll down a rough inclined plane under identical situations. Their time to come down is independent of their ............

$A$ cylinder is rolling down an inclined plane of inclination $30^\circ$ without slipping. Its linear acceleration along the inclined plane will be:

When a uniform solid sphere and a disc of the same mass and of the same radius roll down a rough inclined plane from rest to the same distance,then the ratio of the time taken by them is

Vedclass Test Series

Exam Paper Generator

Online Exam Module