A football of radius R is kept on a hole of r | vedclass

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

Question

(A) Let the radius of the football be $R$ and the radius of the hole be $r$. The diameter of the hole is $2r$. When the plank is tilted at an angle $\

Vedclass · Accepted Answer

$\sin 	heta = \frac{r}{R}$

Vedclass · Answer

(A) Let the radius of the football be $R$ and the radius of the hole be $r$. The diameter of the hole is $2r$. When the plank is tilted at an angle $	heta$,the football rests on the edge of the hole. At the point of impending motion (rolling),the normal force from the other side of the hole becomes zero. Let the center of the football be $O$. The football is in contact with the edge of the hole at a point $P$. The distance from the center $O$ to the point of contact $P$ is $R$. The vertical line passing through the center $O$ makes an angle $	heta$ with the line perpendicular to the plank. In the triangle formed by the center of the football,the center of the hole,and the point of contact,the distance from the center of the hole to the point of contact is $r$. Thus,$\sin 	heta = \frac{r}{R}$. Therefore,the maximum angle $	heta$ for which the football does not roll is given by $\sin 	heta = \frac{r}{R}$.

Similar Questions

$A$ block of mass $M$ is at rest on a plane surface inclined at an angle $\theta$ to the horizontal. The magnitude of the force exerted by the plane on the block is

$A$ block slides down a smooth inclined plane when released from the top,while another falls freely from the same point. Which of the following statements is correct?

Two masses $M_1$ and $M_2$ are attached to the ends of a string which passes over a pulley attached to the top of a double inclined plane of angles of inclination $\alpha$ and $\beta$. If the system is released,the acceleration $a$ of the system is given by:

$A$ body takes $4 \, s$ to reach the bottom of an inclined plane from the top. How much time (in $s$) will it take to cover one-fourth of the distance?

Vedclass Test Series

Exam Paper Generator

Online Exam Module