Question

The condition of no-slip in rotation of a pulley attached to a mass using a string refers to
(A) $v = R\omega $; v is the linear velocity, $\omega $ is the angular velocity and R is the radius
(B) $a = R\alpha $; a is the linear acceleration, $\alpha $ is the angular acceleration and R is the radius
(C) $v = R\omega $and $a = R\alpha $; v is the linear velocity, $\omega $ is the angular velocity, $\alpha $ is the angular acceleration
(D) $T = M\dfrac{{{v^2}}}{R}$; T is the tension in the string, v is the linear velocity, and R is the radius.

Answer 1

Hint: For this question we have to write the expressions for the mass of a pulley attached to a string. In the expression we have to define the quantities that are combined to form the required expression. This will help us to write the answer for the required question.

Complete step by step answer:
We should know that the condition of no-slip in rotation of a pulley attached to a mass using a string is $v = R\omega $ and $a = R\alpha $.
In the above expressions v is the linear velocity, $\omega $ is angular velocity and R is the radius.
Hence we can say that the condition of no-slip in rotation of a pulley attached to a mass using a string refers to $v = R\omega $ and $a = R\alpha $; v is the linear velocity, $\omega $ is the angular velocity, $\alpha $ is the angular acceleration.

So we can say that the correct answer is option C.

Note: We should know that angular acceleration is defined as the time rate of change of the angular velocity and is usually depicted by $\alpha $and is expressed in the unit of radians per second.
From the question we should know that in case of a rope which does not slip relative to the pulley, then there must be a point A which has the same velocity as a point that is at the rim of the pulley. This explanation is necessary to solve questions which involve the no-slip rotation of the pulley.
By pulley we mean that it is a simple machine that consists of a wheel on a fixed axle along with the groove along the edges so as to guide a rope or sometimes a cable.