An object moves in a circular path with a constant speed. Which one of the following statements is correct ?

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Q: 19 (NDA-II/2017)
An object moves in a circular path with a constant speed.
Which one of the following statements is correct ?

question_subject: 

Science

question_exam: 

NDA-II

stats: 

0,5,12,5,6,6,0

keywords: 

{'centripetal acceleration': [1, 0, 0, 1], 'circular path': [0, 0, 1, 2], 'constant speed': [0, 0, 2, 5], 'gentle curve': [0, 0, 0, 1], 'sharp curve': [0, 0, 0, 1], 'curve': [0, 0, 0, 1], 'sharp curves': [0, 0, 0, 1], 'object moves': [0, 0, 0, 4], 'smaller radius': [0, 0, 0, 1], 'larger radius': [0, 0, 0, 1], 'object': [1, 0, 11, 43]}

Option 1: The centripetal acceleration of the object is smaller for a gentle curve (i.e., curve of larger radius) than that for a sharp curve (i.e., curve of smaller radius).

This option is correct. When an object moves in a circular path with a constant speed, the centripetal acceleration is directed towards the center of the circle. It is given by the formula a = v^2 / r, where v is the velocity and r is the radius of the curve. Since the velocity is constant, the centripetal acceleration depends inversely on the radius of the curve. A larger radius means a smaller centripetal acceleration, and vice versa. Therefore, the centripetal acceleration is smaller for a gentle curve (larger radius) compared to a sharp curve (smaller radius).

Option 2: The centripetal acceleration is greater for a gentle curve than that for a sharp curve.

This option is incorrect. As explained earlier, the centripetal acceleration is smaller for a gentle curve (larger radius) than for a sharp curve (smaller radius).

Option 3: The centripetal acceleration is the same for both the gentle and sharp curves.

This option is incorrect. As explained earlier, the centripetal