A solid sphere of radius R undergoes pure rol | vedclass

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

Question

(A) For a body undergoing pure rolling on an inclined plane, the forces acting along the plane are the component of gravity $mg \sin 	heta$ and the f

Vedclass · Accepted Answer

$\frac{g \sin 	heta}{1+\frac{k^2}{R^2}}$

Vedclass · Answer

(A) For a body undergoing pure rolling on an inclined plane, the forces acting along the plane are the component of gravity $mg \sin 	heta$ and the frictional force $f$. The equation of motion is $ma = mg \sin 	heta - f$. The torque equation about the center of mass is $	au = I \alpha = fR$. Since the body is in pure rolling, $\alpha = \frac{a}{R}$. Also, the moment of inertia $I = mk^2$. Substituting these into the torque equation: $mk^2 \cdot \frac{a}{R} = fR$, which gives $f = \frac{ma k^2}{R^2}$. Substituting the expression for $f$ into the force equation: $ma = mg \sin 	heta - \frac{ma k^2}{R^2}$. Rearranging the terms: $ma(1 + \frac{k^2}{R^2}) = mg \sin 	heta$. Therefore, the acceleration is $a = \frac{g \sin 	heta}{1 + \frac{k^2}{R^2}}$.

$A$ solid sphere of radius $R$ undergoes pure rolling down a plane inclined to the horizontal at an angle $\theta$. If the radius of gyration is $k$, then its acceleration is

Similar Questions

One solid sphere and one disc of the same radius are rolling down an inclined plane without slipping. One reaches the bottom earlier than the other due to:

Two identical solid cylinders run a race starting from rest at the top of an inclined plane. If one cylinder slides and the other rolls,which of the following statements is true?

$A$ solid cylinder is suspended symmetrically by two massless strings,as shown in the figure. The distance the cylinder should fall by unbinding the strings to achieve a speed of $4\,ms^{-1}$ is $........cm$. (Take $g=10\,ms^{-2}$)

$A$ sphere undergoes pure rolling on a rough inclined plane with an initial velocity of $2.8 \, m/s$. Find the maximum distance traveled on the inclined plane. (in $m$)

$A$ solid cylinder of mass $M$ and radius $R$ rolls down a smooth inclined plane about its own axis and reaches the bottom with velocity $v$. What is the height of the inclined plane? (Assume $g$ is the acceleration due to gravity.)

Vedclass Test Series

Exam Paper Generator

Online Exam Module