Question

Pulley in the diagram is mass less but there is friction between pulley and string then the
acceleration of system is ___​

Answer 1

Answer:

option A

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Answer 2

Given :

Two blocks of mass = m kg

Block are connected by a string over a pulley

Coefficient of friction between pulley and string = μ

To Find:

Acceleration of the system.

Solution:

• If we make the Free Body Diagram(FBD) of the system we get:

1. Force mg acting downwards on the block hanging from the pulley.
2. Tension T in the string acting upwards on the hanging mass.
3. Tension T in the string acting right from the mass on the plane.
4. Friction f acting left from the mass on the plane.
5. Normal acting upwards on mass on the plane, balanced by mg acting downwards on the mass.

• Let us assume mass hanging from pulley moves down with acceleration 'a'.
• Equating all the forces:

                       ma = mg - T                         (Force = mass × acceleration)

                    ⇒ T = mg - ma              (1)

• Similarly, mass on the plane will move right with acceleration a

                                 ma = T - f

                               But, f = μN

                             and, N = mg

                                 ⇒ f = μmg

                        So, ma = T - μmg                      

                            ⇒ T = ma + μmg                 (2)

• Equating (1) and (2):

                       mg - ma = ma + μmg

                         ⇒ 2ma = mg - μmg

                         ⇒ 2a = g(1 - μ)

                         ⇒ a = $\frac{g(1 - u)}{2}$

Therefore, acceleration of the system is option (A) $\frac{g(1 - u)}{2}$.