
The wheel radius rolls to right without slipping and has a velocity of its center . The speed of the point on the wheel for the instant represented in the figure is:

A)
B)
C)
D)
Answer
151.2k+ views
Hint: In this question, we have to use the analytical method to find the velocity at the point . In the analytical method, we use vectors and calculate the speed at a particular instant. We use the parallelogram method to analyze the vector. Velocity is a vector quantity and can be calculated using the vector analysis method.
Formula used:
Where and are two vectors inclined to each other at a particular angle.
is the angle between the two vectors.
is the resultant vector of the two vectors and
(where is the velocity, is the radius and is the angular velocity)
Complete step by step solution:

The wheel is in a uniform circular motion. It is rolling with a velocity .
We know that the linear speed of an object moving in a circular motion is
Where is the radius of the wheel and is the angular velocity
We can find the angular velocity of the from the linear velocity as,
(Given )
Given
The velocity at a point is
=
The total velocity at the instant is can be obtained by using the formula,
……………………………(1)
Here, and the angle between and is that is obtained from the figure.
The net velocity can be obtained by substituting the values in the equation
Calculating the values,
The answer is Option (A): .
Note: An object is in a uniform circular motion if it moves along the circumference of a circle with constant speed. The right-hand grip rule states that if the curvature of the fingers of the right hand represents the sense of rotation then the thumb represents the direction of the angular displacement vector. Angular velocity is defined as the time rate of angular displacement.
Formula used:
Where
Complete step by step solution:

The wheel is in a uniform circular motion. It is rolling with a velocity
We know that the linear speed of an object moving in a circular motion is
Where
We can find the angular velocity of the from the linear velocity as,
Given
The velocity at a point
The total velocity at the instant is can be obtained by using the formula,
Here,
The net velocity
Calculating the values,
The answer is Option (A):
Note: An object is in a uniform circular motion if it moves along the circumference of a circle with constant speed. The right-hand grip rule states that if the curvature of the fingers of the right hand represents the sense of rotation then the thumb represents the direction of the angular displacement vector. Angular velocity is defined as the time rate of angular displacement.
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