Q. A block X of mass 0.5 kg is held by a long massless string on a frictionless inclined plane of inclination 30 to the horizontal. The string is wound on a uniform solid cylindrical drum Y of mass 2 kg and of radius 0.2 mas shown in figure.
The drum is given an initial angular velocity such that the block X starts moving up the plane.
(a) Find the tension in the string during the motion.
(b) At a certain instant of time the magnitude of the angular velocity o ff is . Calculate the distance travelled by X from that instant of time until it comes to rest. Physics Question Image

 2391  193 IIT JEEIIT JEE 1994System of Particles and Rotational Motion Report Error

Solution:

Given, mass of block X , m= 0.5kg
Mass of drum Y, M = 2kg
Radius of drum, R = 0.2 m
Angle of inclined plane,
(a) Let a be the linear retardation of block X and be the angular retardation of drum Y. Then,

...(i)
or ...(ii)

or ....(iii)
Solving Eqs. (i), (ii) and (iii) for T, we get,

Substituting the value we get,


(b) From Eq. (iii), angular retardation of drum

or linear retardation of block

At the moment when angular velocity of drum is

The linear velocity of block will be

Now, the distance (s) travelled by the block until it comes to rest will be given by


or

Solution Image