Q.

The direction of angular acceleration of a body moving in a circle in the plane of the paper is 

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a

along the perpendicular to the plane of the paper 
 

b

along the radius outward 
 

c

along the radius inward 
 

d

along the tangent 
 

answer is D.

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Detailed Solution

The direction of angular acceleration indicates how quickly an object's rotational speed changes and the axis along which this change occurs. To determine this direction for a body moving in a circle on the plane of the paper, we use the right-hand rule.

Applying the Right-Hand Rule:

  1. Identify the Rotation Direction: Observe the direction in which the object is rotating.
  2. Position Your Right Hand: Extend your right hand with fingers pointing in the direction of rotation.
  3. Curl Your Fingers: Curl your fingers following the rotation's direction.
  4. Thumb Direction: Your thumb, extended perpendicular to your curled fingers, points in the direction of the angular velocity vector.

If the object's rotational speed is changing, the direction of angular acceleration aligns with the change in angular velocity:

  • Increasing Rotational Speed: The direction of angular acceleration matches the angular velocity vector.
  • Decreasing Rotational Speed: The direction of angular acceleration opposes the angular velocity vector.

In both cases, the direction of angular acceleration is perpendicular to the plane of the paper. This perpendicular orientation arises because angular quantities like angular velocity and angular acceleration are vector quantities that point along the axis of rotation, as determined by the right-hand rule.

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