Home
Class 12
PHYSICS
In a continuous printing process paper i...

In a continuous printing process paper is drawn into the press at a constant speed v. Denoting by 'r' the radius of the paper roll at any given time and by 'b' the thickness of the paper. What is the angular acceleraion of the paper roll?

A

`(bv^(2))/(2pir^(3))`

B

`(2bv^(2))/(pir^(3))`

C

`(bv^(2))/(4pir^(3))`

D

`(4bv^(2))/(pir^(3))`

Text Solution

Verified by Experts

The correct Answer is:
A
Let one layer of paper be unrolled
`vDeltat =2pir and Deltar=-b`
`(Deltar)/(Deltat)=(-bv)/(2pir)=(dr)/(dt)`
`alpha=(domega)/(dt)=(d)/(dt)((v)/(r ))`
`=(1)/(r)(dv)/(dt)+v(d)/(dt)((1)/(r))`
`= 0 -(v)/(r^(2))(dr)/(dt)`
`=(-(v)/(r^(2)))(-(bv)/(2pir))`
`(bv^(2))/(2pir^(3))`
`alpha=(bv^(2))/(2pir^(3)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

A square sheet of paper is converted into a cylinder by rolling it along its side.What is the ratio of the base radius to the side of the square?

A rectangular sheet of paper 44 cm xx 18 cm is rolled along its length and a cylinder is formed. Find the radius of the cylinder.

Knowledge Check

  • Density of the material of a paper is given a 0.5 g cm^(-3) . The mass of the paper is 1 g and its length and breadth are 10 c and 5 cm, respectively. Arrange the following steps in a sequence to find the thickness of the paper. (A). The 0thickness of the paper is ("Volume of the paper (m)")/("Vlume of the paper (V)") (B) The density (d) of the material of the paper is =("Mass of the paper (m)")/("volume of the paper (V)") (C). then the volume (V) o the paper =("Mass of the paper (m)")/("Density (d) of the paper") (D). The volume (V) of the paper is=length xx breadth xx thickness of the paper.

    A
    ABCD
    B
    BADC
    C
    ABDC
    D
    BCDA

  • A disc of the radius R is confined to roll without slipping at A and B. If the plates have the velocities v and 2v as shown, the angular velocity of the disc is

    A
    `(3V)/(2R)` Anticlockwise
    B
    `(3V)/(2R)` Clockwise
    C
    `(V)/(2R)` Anticlockwise
    D
    `(V)/(2R)` clockwise

  • A sphere of mass M rolls without slipping on rough surface with centre of mass has constant speed v_0 . If mass of the sphere is m and its radius be R , then the angular momentum of the sphere about the point of contact is.

    A
    `(4)/(5) Mv_0R(- hat k)`
    B
    `(9)/(5) Mv_0 R(- hat k)`
    C
    `(8)/(5) Mv_0 R(- hat k)`
    D
    `(7)/(5) Mv_0 R (- hat k)`

    • Similar Questions

    Explore conceptually related problems

    A rectangular sheat of paper 44cm xx18cm is a rolled along its length and a cylinder is formed.Find the radius of the cylinder.

    A rectangular sheat of paper 44cm xx18cm is rolled along its length and a cylinder is formed.Find the radius of the cylinder.

    A rectangular paper of 44 cm long and 6 cm wide is rolled to form a cylinder of height equal to width of the paper. The radius of the base of the cylinder so rolled is

    A piece of paper is in the form of a sector, making an angle a. The paper is rolled to form a right circular cone of radius 5 cm and height 12 cm. Then the value of angle a is

    A ring of radius R is rolling purely on the outer surface of a pipe of radius 4R At some instant the center of the ring has constant speed =v then the acceleration of the point on the ring which is in contact with the surface of the pipe is

    Home
    Profile