From an inclined plane,a sphere,a disc,a ring | vedclass

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

Question

(C) The time taken by a rolling body to reach the bottom of an inclined plane is given by:$t = \frac{1}{\sin 	heta} \sqrt{\frac{2 h}{g} \left(1 + \fr

Vedclass · Accepted Answer

Sphere,disc,shell,ring

Vedclass · Answer

(C) The time taken by a rolling body to reach the bottom of an inclined plane is given by:$t = \frac{1}{\sin 	heta} \sqrt{\frac{2 h}{g} \left(1 + \frac{K^2}{R^2}ight)}$Since $	heta$,$h$,and $g$ are constant for all bodies,the time taken is proportional to $\sqrt{1 + \frac{K^2}{R^2}}$.We calculate the values of $\frac{K^2}{R^2}$ for each object:For a ring: $\frac{K^2}{R^2} = 1$For a disc: $\frac{K^2}{R^2} = \frac{1}{2} = 0.5$For a solid sphere: $\frac{K^2}{R^2} = \frac{2}{5} = 0.4$For a spherical shell: $\frac{K^2}{R^2} = \frac{2}{3} \approx 0.67$Comparing these values,we get: $\left(\frac{K^2}{R^2}ight)_{	ext{sphere}} Therefore,the order of time taken is: $t_{	ext{sphere}} < t_{	ext{disc}} < t_{	ext{shell}} < t_{	ext{ring}}$.

From an inclined plane,a sphere,a disc,a ring,and a spherical shell of the same radius are rolled without slipping from the same height simultaneously. The order of their reaching at the base will be:

Similar Questions

$A$ cylinder rolls down two different inclined planes of the same height but of different inclinations.

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 ............

$A$ 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 $\,m/s$)

$A$ 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

$A$ solid spherical ball is rolled up an inclined plane of angle of inclination $30^{\circ}$ with an initial speed of $4 \ m/s$ at the bottom of the inclination. How far will the ball go up the plane (in $cm$)? (Use $g=10 \ m/s^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module