Inner and outer radii of a spool are r and R | vedclass

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

Question

(C) For pure rolling,the velocity of the point of contact with the ground must be zero. When a force $F$ is applied to the thread wound on the inner r

Vedclass · Accepted Answer

Thread winds,spool moves to the right and friction acts rightwards.

Vedclass · Answer

(C) For pure rolling,the velocity of the point of contact with the ground must be zero. When a force $F$ is applied to the thread wound on the inner radius $r$ as shown,it creates a torque about the center of mass that tends to rotate the spool clockwise. As the spool rotates clockwise,the point of contact with the ground has a tendency to slip to the left. To oppose this,the static friction $f$ acts towards the right. However,let's analyze the torque about the point of contact $P$. The torque due to force $F$ is $	au_P = F(R-r)$ in the clockwise direction. Since this torque is non-zero,the spool will have an angular acceleration $\alpha$ in the clockwise direction. For pure rolling,the spool must move to the right with acceleration $a_{cm} = \alpha R$. Considering the forces: $F + f = m a_{cm}$ (where $f$ is friction acting to the right). Considering torque about the center of mass: $F r + f R = I \alpha$. Since the spool moves to the right and rotates clockwise,the thread winds further. Thus,the spool moves to the right and friction acts to the right.

Inner and outer radii of a spool are $r$ and $R$ respectively. $A$ thread is wound over its inner surface and placed over a rough horizontal surface. The thread is pulled by a force $F$ as shown in the figure. Then,in the case of pure rolling:

Similar Questions

$A$ sphere of mass $M$ and radius $R$ is attached by a light rod of length $l$ to a point $P$. The sphere rolls without slipping on a circular track as shown. It is released from the horizontal position. The angular momentum of the system about $P$ when the rod becomes vertical is:

On a solid sphere lying on a horizontal surface,a force $F$ is applied at a height of $R/2$ from the centre of mass. The initial acceleration of a point at the top of the sphere is (there is no slipping at any point).

$A$ thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of:

The total kinetic energy of a body of mass $10 \ kg$ and radius $0.5 \ m$ moving with a velocity of $2 \ m/s$ without slipping is $32.8 \ J$. The radius of gyration of the body is .......... $m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module