A wheel of radius 20 cm is pushed ot move it on a rough horizontal surface. It is found to move through a distance of 60 cm on the road during the time it completes one revolutionabout the centre. Assume that the linear and the angular accelerations are uniform. The frictional force acting on the wheel by the surface is

Options

A. along the velocity of the wheel
B. opposite to the velocity o the wheel
C. perpendicular to the velocity of the wheel
D. zero

Answer

To solve the problem, we need to analyze the motion of the wheel and the forces acting on it. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Given Information
- The radius of the wheel (R) = 20 cm = 0.2 m
- The distance traveled by the wheel in one complete revolution = 60 cm = 0.6 m
- The circumference of the wheel (C) = 2πR = 2π(0.2 m) = 0.4π m ≈ 0.628 m

### Step 2: Compare the Distance Traveled with the Circumference
The distance traveled (0.6 m) is less than the circumference of the wheel (approximately 0.628 m). This indicates that the wheel is slipping as it rolls.

### Step 3: Analyze the Motion
Since the wheel is rolling on a rough surface and the distance traveled is less than the circumference, it suggests that the translational speed of the wheel (Vt) is less than the rotational speed (Vr) at the point of contact.

### Step 4: Determine the Direction of Friction
The frictional force acts to oppose the relative motion between the wheel and the surface. Since the wheel is slipping, the frictional force will act in the direction of the translational motion (the direction the wheel is rolling).

### Step 5: Conclude the Direction of Frictional Force
Since the translational velocity (Vt) is less than the rotational velocity (Vr), the frictional force must act in the direction of Vt. Therefore, the frictional force is along the direction of the wheel's movement.

### Step 6: Identify the Correct Option
From the options provided, the correct option states that the frictional force acting on the wheel is along the velocity of the wheel.

### Final Answer
The frictional force acting on the wheel by the surface is directed along the velocity of the wheel.

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