The following bodies,(1) a ring(2) a disc(3) | vedclass

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

Question

(C) For a body of mass $m$ and radius $R$ rolling down an inclined plane of angle $	heta$,the acceleration $a$ is given by $a = \frac{g \sin 	heta}{

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) For a body of mass $m$ and radius $R$ rolling down an inclined plane of angle $	heta$,the acceleration $a$ is given by $a = \frac{g \sin 	heta}{1 + \frac{k^2}{R^2}}$,where $k$ is the radius of gyration.The time taken to reach the bottom of an inclined plane of length $S$ is $t = \sqrt{\frac{2S}{a}} = \sqrt{\frac{2S}{g \sin 	heta} \left(1 + \frac{k^2}{R^2}ight)}$.For the time $t$ to be minimum,the ratio $\frac{k^2}{R^2}$ must be minimum.Comparing the values of $\frac{k^2}{R^2}$ for the given bodies:$(1)$ Ring: $k^2 = R^2 \Rightarrow \frac{k^2}{R^2} = 1$$(2)$ Disc: $k^2 = \frac{R^2}{2} \Rightarrow \frac{k^2}{R^2} = 0.5$$(3)$ Solid cylinder: $k^2 = \frac{R^2}{2} \Rightarrow \frac{k^2}{R^2} = 0.5$$(4)$ Solid sphere: $k^2 = \frac{2R^2}{5} \Rightarrow \frac{k^2}{R^2} = 0.4$Since the solid sphere has the minimum value of $\frac{k^2}{R^2}$,it will have the maximum acceleration and will reach the bottom of the inclined plane first.

Similar Questions

$A$ uniform solid sphere of mass $m$ and radius $r$ rolls without slipping down an inclined plane,inclined at an angle $45^o$ to the horizontal. Find the minimum magnitude of the frictional coefficient required for rolling without slipping.

$A$ ring,a solid sphere,and a disc are rolling down from the top of an inclined plane of the same height. What is the sequence in which they reach the surface?

$A$ disc rolls without slipping down an inclined plane of length $L$ and inclination $\theta$. What will be its velocity at the bottom?

$A$ solid cylinder and a solid sphere having the same mass and radius roll down on the same smooth inclined plane. The ratio of the acceleration of the cylinder $(a_c)$ to that of the sphere $(a_s)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module