Question

Which of the following is TRUE for a particle traveling a circular path at a constant speed?

The choices are listed below. YOU MAY CHOOSE MORE THAN ONE.

a) The velocity of the particle is different at different points on the circular path.

b) The acceleration is directed tangent to the path.

c) The magnitude of the acceleration is constant.

e) The particle must be moving faster if the radius of curvature is smaller.

f) The particle is decelerating if the radius of curvature is higher.

e) The mass of the particle does not affect the speed at which it travels.

Answer 1

The question says that the particle moves in a circular path at constant speed 

⇒ The particle is describing a uniform circular motion 

⇒ Tangential acceleration = 0

Now check the options 

A) is correct because velocity is a vector quantity and it changes when there is a change in direction.

B) is incorrect because in uniform circular motion tangential acceleration is zero and the acceleration is acted only towards the radial direction and the velocity is tangential.

C) is correct because in uniform circular motion the acceleration acts only along the radial direction which is  a_n = w² r .

D) is incorrect because if we take radial acceleration (a_n) constant then the velocity of particle (in terms of radius of curvature will be v² = r * a_n) will decrease.

E) is incorrect because Tangential speed is proportional to the radius , that means by decreasing the radius the tangential speed will also decrease but it will never decelerate the particle.

F) is correct because we don't have mass in the relation of speed (i.e v² = r * a_n). 

 THANK YOU