Home
Class 11
PHYSICS
A carpet of mass m made of inextensible ...

A carpet of mass m made of inextensible material is rolled along its length in the form of a cylinder of radius r and kept on a rough floor. The decrease in the potential energy of the system, when the carpet is unrolled to a radius `(r)/(2)` without sliding is (g =acceleration due to gravity)

A

`(3)/(4) mgr`

B

`(5)/(8) mgr`

C

`(7)/(8) mgr`

D

`(1)/(2) mgr`

Text Solution

Verified by Experts

The correct Answer is:
C
Mass left over unrolled `= (m)/(pi r^(2)) xx pi ((r)/(2))^(2)= (m)/(4)`
decrease in P.E. `= mgr- ((m)/(4))g (r)/(2)= (7)/(8) mgr`
Promotional Banner

Similar Questions

Explore conceptually related problems

A floor-mat of mass M made up of extensible material, is rolled along its length so as to form a cylinder of radius R and kept on a rough horizontal surface. If the mat is now unrolled, without sliding, to a radius (R )/(2) , the decrease in potential energy is

A carpet of mass M made of inextensible material is rolled along its length in the form of a cylinder of radius R and is kept on a graph floor. The carpet. Starts unrolling without sliding on the floor when a negligible small push is given to it. Calculate the horizontal velcoity of the axis of the cylindrical part of the carpet when its radius reduces to R//2 .

A carpet of mass M is rolled along its length so as to from a cylinder of radius R and is kept on a rough floor. When a negligibly small push is given to the cylindrical carpet, it stars unrolling itself without sliding on the floor. Calculate horizontal velocity of cylindrical part of the carpet when its radius reduces to R//2 .

The binding energy of an object of mass m placed on the surface of the earth r is (R = radius of earth, g = acceleration due to gravity)

Find the binding energy of a satellite of mass m in orbit of radius r , (R = radius of earth, g = acceleration due to gravity)

A cylinder of mass M and radius R rolls on an inclined plane. The gain in kinetic energy is

A particle of mass m performs vertical motion in a circle of radius r. Its potential energy at the highest point is ….. " " ( g is acceleration due to gravity)

The condition for a uniform spherical mass m of a radius r to be a black hole is [ G =gravitational constant and g =acceleration due to gravity]