A particle is moving in a circular path of radius r at a constant speed v. Which one of the following graphs correctly represents its acceleration a?

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Q: 49 (NDA-II/2014)
A particle is moving in a circular path of radius r at a constant speed v.
Which one of the following graphs correctly represents its acceleration a?

question_subject: 

Science

question_exam: 

NDA-II

stats: 

0,0,3,1,0,2,0

keywords: 

{'circular path': [0, 0, 1, 2], 'graphs': [0, 0, 1, 0], 'particle': [0, 2, 8, 30], 'constant speed': [0, 0, 2, 5]}

Option 4 correctly represents the acceleration of a particle moving in a circular path of radius r at a constant speed v.

In a circular motion, the acceleration of the particle is directed towards the center of the circle, and its magnitude is given by the equation a = v^2 / r, where v is the velocity of the particle and r is the radius of the circle.

Option 1 shows a constant non-zero acceleration, which does not match the characteristics of a particle moving in a circular path at a constant speed.

Option 2 shows an increasing acceleration, which is incorrect because the acceleration in a circular motion remains constant.

Option 3 shows a decreasing acceleration, which is also incorrect because the acceleration in a circular motion remains constant.

Option 4 correctly shows the acceleration decreasing as the radius of the circle increases. This is because the equation for acceleration in circular motion (a = v^2 / r) shows that the acceleration is inversely proportional to the radius.