A force of 49 N acts tangentially at the hig | vedclass

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

Question

(A) Let $F = 49 \ N$ be the applied force,$m = 20 \ kg$ be the mass of the solid sphere,and $r$ be its radius.For a solid sphere,the moment of inertia

Vedclass · Accepted Answer

$3.5$

Vedclass · Answer

(A) Let $F = 49 \ N$ be the applied force,$m = 20 \ kg$ be the mass of the solid sphere,and $r$ be its radius.For a solid sphere,the moment of inertia about its center of mass is $I_{cm} = \frac{2}{5} mr^2$.The moment of inertia about the point of contact (bottom point) is $I = I_{cm} + mr^2 = \frac{2}{5} mr^2 + mr^2 = \frac{7}{5} mr^2$.The torque about the point of contact is $	au = F 	imes (2r)$.Using $	au = I \alpha$,we have $F 	imes 2r = (\frac{7}{5} mr^2) \alpha$.$49 	imes 2r = \frac{7}{5} 	imes 20 	imes r^2 	imes \alpha$.$98r = 28r^2 \alpha$.Since the sphere rolls without slipping,the linear acceleration $a$ of the center is $a = r \alpha$,so $\alpha = \frac{a}{r}$.Substituting this into the equation: $98r = 28r^2 (\frac{a}{r}) = 28ra$.$98 = 28a$.$a = \frac{98}{28} = 3.5 \ m/s^2$.

$A$ force of $49 \ N$ acts tangentially at the highest point of a solid sphere of mass $20 \ kg$,kept on a rough horizontal plane. If the sphere rolls without slipping,then the acceleration of the center of the sphere is (in $m/s^2$)

Similar Questions

$A$ wheel of radius $r$ rolls without slipping with a speed $v$ on a horizontal road. When it is at a point $A$ on the road,a small piece of mud separates from the wheel at its highest point $B$ and drops at point $C$ on the road. The distance $AC$ will be

$A$ hollow sphere of mass $2 \, kg$ and diameter $0.2 \, m$ is rolling on an inclined plane with a velocity of $0.5 \, m/s$. The kinetic energy of the sphere will be .......... $J$.

$A$ horizontal force $F$ is applied at the center of a sphere as shown in the figure. The coefficient of friction between the sphere and the ground is $\mu$. What is the maximum value of $F$ if the sphere does not slip?

$A$ solid sphere of mass $1\,kg$ rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3}\,J$. The speed of the centre of mass of the sphere is $.........\,cm\,s^{-1}$.

$A$ sphere of mass $M$ and radius $r$ slips on a rough horizontal plane. At some instant,it has translational velocity $V_0$ and rotational velocity about the centre $\frac{V_0}{2r}$. The translational velocity when the sphere starts pure rolling motion is

Vedclass Test Series

Exam Paper Generator

Online Exam Module