Question

In a disc rolling on a surface with no-slip condition being satisfied, the following statement is true
(A) The velocity and acceleration of the point of contact is zero
(B) The velocity of the point of contact is zero and the acceleration of the point of contact is greater than zero.
(C) The velocity of the point of contact is greater than zero and the acceleration of the point of contact is zero
(D) The velocity and acceleration of the point of contact is greater than zero

Answer 1

Rolling without slipping is a combination of translation and rotation. In this case, the point of contact is instantaneously at rest. The object will also move in a straight line in the absence of a net external force. For the instantaneous velocity to be zero, the condition $v = R\omega$ must be true.
Here, $v$ is the linear velocity of the disc.
$R$ is the radius of the disc.
And $\omega$ is the angular velocity of the disc.

Complete step by step answer:
For rolling without slipping, the velocity at the point of contact is zero or the point in contact of the disc with the ground is stationary. This will be true, only if the linear velocity at the point of contact is equal to $v = R\omega$
The point of contact has two accelerations:
Tangential acceleration: Due to rotation of the disc there will be tangential acceleration which is given as ${a_T} = R\alpha$
Here, ${a_T}$ is the tangential acceleration,
$\alpha$ is the angular acceleration of the disc with respect to ground.
(ii) Normal acceleration: The direction of normal acceleration always passes through the center of mass of the disc.
Both the accelerations are perpendicular to each other. Thus, the net acceleration is not zero at the point of contact and it is at some angle depending on the value of the accelerations.
As acceleration of the point is contact is not zero and the velocity at the point of contact is zero

Therefore, option B is the correct option.

Note: The net acceleration of the disc is not zero and the direction of the net acceleration is given by taking the resultant vector of both the accelerations. The point of contact is always at rest and thus it’s instantaneous velocity is always zero. In cases of rolling without slipping the linear velocity is given as $v = R\omega$ .