Home
Class 11
PHYSICS
Effect of friction between pulley and th...

Effect of friction between pulley and thread :
In ideal cases i.e., when pulley and strings are massless and no friction exists at any contact surface, then tension in the string is constant throughout its length. But consider a, massless pulley and massless string but friction exists between pulley and string With coefficient `mu`. Then tension at the two ends of the pulley will be different. As shown in figure, consider an element of string :
`dN=(T+dT) "sin" (d theta)/2+T "sin"(d theta)/2`

`(T+dT)"cos"(d theta)/2 -T"cos"(d theta)/2-mu dN=dr a=0` (massless strings)
`dT"cos"(d theta)/2=mu dN`
`dT"cos"(d theta)/2=mu [(T+dt) "sin" (d theta)/2+T "sin" (d theta)/2]`
`dt."cos" (d theta)/2=mu[T "sin" (d theta)/2+dT. "sin" (d theta)/2+T "sin" (d theta)/2]`
`dT=mu[T. (d theta)/2+0+T(d theta)/2]=mu T cos theta`
int_(T_(1))^(T_(2)) (d T)/T=int _(0)^(pi)mu d theta rArr ln(T_(2)/T_(1))=mu pi rArrT_(2)/T_(1)=e^(mu pi)`
Suppose cofficient of friction between the string and pulley is `mu =1/pi`
What should be the ratio of heavier mass to lighter mass for no motion ?

A

`e`

B

`1/e`

C

`e^(L)`

D

`e^(R)`

Text Solution

Verified by Experts

The correct Answer is:
a
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • FORCE ANALYSIS

    ANURAG MISHRA|Exercise Matching type|13 Videos
  • FORCE ANALYSIS

    ANURAG MISHRA|Exercise Level-2|73 Videos
  • DESCRIPTION OF MOTION

    ANURAG MISHRA|Exercise Level-3|34 Videos
  • IMPULSE AND MOMENTUM

    ANURAG MISHRA|Exercise matching|3 Videos

Similar Questions

Explore conceptually related problems

Find the acceleration blocks in fig. The pulley and the string are massless.

Find the acceleration and tension in the string in the following cases . The pulley and string are massless. (a) (b)

Knowledge Check

  • Effect of friction between pulley and thread : In ideal cases i.e., when pulley and strings are massless and no friction exists at any contact surface, then tension in the string is constant throughout its length. But consider a, massless pulley and massless string but friction exists between pulley and string With coefficient mu . Then tension at the two ends of the pulley will be different. As shown in figure, consider an element of string : dN=(T+dT) "sin" (d theta)/2+T "sin"(d theta)/2 (T+dT)"cos"(d theta)/2 -T"cos"(d theta)/2-mu dN=dr a=0 (massless strings) dT"cos"(d theta)/2=mu dN dT"cos"(d theta)/2=mu [(T+dt) "sin" (d theta)/2+T "sin" (d theta)/2] dt."cos" (d theta)/2=mu[T "sin" (d theta)/2+dT. "sin" (d theta)/2+T "sin" (d theta)/2] dT=mu[T. (d theta)/2+0+T(d theta)/2]=mu T cos theta int_(T_(1))^(T_(2)) (d T)/T=int _(0)^(pi)mu d theta rArr ln(T_(2)/T_(1))=mu pi rArrT_(2)/T_(1)=e^(mu pi) Suppose cofficient of friction between the string and pulley is mu =1/pi The tension on side ofheavier\nass will be:

    A
    `m_(1)g`
    B
    `m_(2)g`
    C
    `(2m_(2)g)/3`
    D
    `(2m_(1)g)/3`
  • Effect of friction between pulley and thread : In ideal cases i.e., when pulley and strings are massless and no friction exists at any contact surface, then tension in the string is constant throughout its length. But consider a, massless pulley and massless string but friction exists between pulley and string With coefficient mu . Then tension at the two ends of the pulley will be different. As shown in figure, consider an element of string : dN=(T+dT) "sin" (d theta)/2+T "sin"(d theta)/2 (T+dT)"cos"(d theta)/2 -T"cos"(d theta)/2-mu dN=dr a=0 (massless strings) dT"cos"(d theta)/2=mu dN dT"cos"(d theta)/2=mu [(T+dt) "sin" (d theta)/2+T "sin" (d theta)/2] dt."cos" (d theta)/2=mu[T "sin" (d theta)/2+dT. "sin" (d theta)/2+T "sin" (d theta)/2] dT=mu[T. (d theta)/2+0+T(d theta)/2]=mu T cos theta int_(T_(1))^(T_(2)) (d T)/T=int _(0)^(pi)mu d theta rArr ln(T_(2)/T_(1))=mu pi rArrT_(2)/T_(1)=e^(mu pi) Suppose cofficient of friction between the string and pulley is mu =1/pi The tension on side of lighter mass will be:

    A
    `m_(1)g`
    B
    `m_(2)g`
    C
    `(2m_(2)g)/3`
    D
    `(4m_(1)g)/3`
  • Effect of friction between pulley and thread : In ideal cases i.e., when pulley and strings are massless and no friction exists at any contact surface, then tension in the string is constant throughout its length. But consider a, massless pulley and massless string but friction exists between pulley and string With coefficient mu . Then tension at the two ends of the pulley will be different. As shown in figure, consider an element of string : dN=(T+dT) "sin" (d theta)/2+T "sin"(d theta)/2 (T+dT)"cos"(d theta)/2 -T"cos"(d theta)/2-mu dN=dr a=0 (massless strings) dT"cos"(d theta)/2=mu dN dT"cos"(d theta)/2=mu [(T+dt) "sin" (d theta)/2+T "sin" (d theta)/2] dt."cos" (d theta)/2=mu[T "sin" (d theta)/2+dT. "sin" (d theta)/2+T "sin" (d theta)/2] dT=mu[T. (d theta)/2+0+T(d theta)/2]=mu T cos theta int_(T_(1))^(T_(2)) (d T)/T=int _(0)^(pi)mu d theta rArr ln(T_(2)/T_(1))=mu pi rArrT_(2)/T_(1)=e^(mu pi) Suppose cofficient of friction between the string and pulley is mu =1/pi If m_(2)=2em then acceleration of each mass is :

    A
    `g`
    B
    `g//3`
    C
    `eg//3`
    D
    zero
  • Similar Questions

    Explore conceptually related problems

    Find the accelerations of two blocks. Assume pulleys and strings are massless and frictionless. Also assume the string to be inextensible.

    The tension in the string in the pulley system shown in .

    Pulleys and strings are massless. The horizontal surface is smooth. What is the acceleration of the block

    Pulleys and strings are massless.The horizontal surface is smooth.What is the acceleration of the block

    In the arrangement shown, the pulleys and strings are massless. The acceleration of block B is :