A cylinder of mass M and radius r is mounted | vedclass

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

Question

(D) Let $a$ be the linear acceleration of the bucket and $T$ be the tension in the rope. For the bucket of mass $m$,the equation of motion is: $mg - T

Vedclass · Accepted Answer

$\frac{2mg}{M + 2m}$

Vedclass · Answer

(D) Let $a$ be the linear acceleration of the bucket and $T$ be the tension in the rope. For the bucket of mass $m$,the equation of motion is: $mg - T = ma$  --- $(1)$ For the cylinder of mass $M$ and radius $r$,the torque $	au$ is given by $	au = I\alpha$,where $I = \frac{1}{2}Mr^2$ is the moment of inertia of the cylinder and $\alpha = \frac{a}{r}$ is the angular acceleration. The torque is also given by $	au = Tr$. Equating the two expressions for torque: $Tr = (\frac{1}{2}Mr^2)(\frac{a}{r}) = \frac{1}{2}Mra$. Thus,$T = \frac{1}{2}Ma$ --- $(2)$ Substituting the value of $T$ from equation $(2)$ into equation $(1)$: $mg - \frac{1}{2}Ma = ma$ $mg = ma + \frac{1}{2}Ma = a(m + \frac{M}{2}) = a(\frac{2m + M}{2})$ $a = \frac{2mg}{M + 2m}$

$A$ cylinder of mass $M$ and radius $r$ is mounted on a frictionless axle over a well. $A$ rope of negligible mass is wrapped around the cylinder and a bucket of mass $m$ is suspended from the rope. The linear acceleration of the bucket will be

Similar Questions

$A$ cylinder of mass $M$ and radius $r$ is mounted on a frictionless axle over a well. $A$ rope of negligible mass is wrapped around the solid cylinder and a bucket of mass $m$ is suspended from the rope. The linear acceleration of the bucket will be

$A$ uniform rod of mass $m$ and length $l$ is suspended by means of two identical inextensible light strings as shown in the figure. The tension in one string immediately after the other string is cut is . . . . . . . ($g$ is the acceleration due to gravity)

In pure translational motion,the velocity of every particle of a body at any instant is what? Equal or unequal?

What is rotational motion? Explain it with an example.

Vedclass Test Series

Exam Paper Generator

Online Exam Module