A body is uniformly rotating about an axis fixed in an inertial frame

1.	A body is uniformly rotating about an axis fixed in an inertial frame of reference. Let A be a unit vector along the axis of rotation and B be the unit vector along the resultant force on a particle P of the body away from the axis. The value of A.B is(a) 1 (b) -1 (c) 0 (d) None of these.
Answer» Answer ⇒ Option (c). 0 Explanation ⇒ According to the QUESTION, the BODY is uniformly ROTATING thus the resultant FORCE on the particle P will be in the radial direction. ∴ The DIRECTIONS of A and B will be perpendicular to each other. Mathematically, Angle between them = θ = 90° ∴ A.B = \|A\|.\|B\|. Cos90° [A.B. is the dot product of vectors.] = \|A\|.\|B\|. 0 = 0 Hence, the answer is Option (c). Hope it helps.

A body is uniformly rotating about an axis fixed in an inertial frame of reference. Let A be a unit vector along the axis of rotation and B be the unit vector along the resultant force on a particle P of the body away from the axis. The value of A.B is(a) 1 (b) -1 (c) 0 (d) None of these.

Answer»

Answer ⇒ Option (c). 0

Explanation ⇒ According to the QUESTION, the BODY is uniformly ROTATING thus the resultant FORCE on the particle P will be in the radial direction.

∴ The DIRECTIONS of A and B will be perpendicular to each other.

Mathematically,

Angle between them = θ = 90°

∴ A.B = |A|.|B|. Cos90° [A.B. is the dot product of vectors.]

= |A|.|B|. 0

= 0

Hence, the answer is Option (c).

Hope it helps.

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A body is uniformly rotating about an axis fixed in an inertial frame of reference. Let A be a unit vector along the axis of rotation and B be the unit vector along the resultant force on a particle P of the body away from the axis. The value of A.B is(a) 1 (b) -1 (c) 0 (d) None of these.

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