Question

A solid cylinder has a thin string wrapped several times around its circumference. The string is fixed at one end and the cylinder is released. Find the downward acceleration of cylinder and tension in the string.

Answer 1

Answer:

PHYSICS

A string is wrapped several times round a solid cylinder and then the end of the string is held stationary while the cylinder is released from rest with an initial motion. The acceleration of the cylinder and tension in the string will be

A .

32gand3mg

B .

gand2mg

C .

3gand2mg

D .

2gand3mh

Let the mass of cylinder is m and radius of it is r.

so, moment of inertia of cylinder , I=21mr2

torque = moment of inertia * angular acceleration

force * displacement =21mr2×ra

we know, linear acceleration, a = r * angular acceleration

T×r=21mr×a

T=21ma ......(1) 

now, net force = ma 

weight - tension = ma 

or, mg−21ma=ma

or, mg=