An object moves in a circular path with a constant speed. Which one of

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

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).

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

The centripetal acceleration is the same for both, the gentle and sharp curves.

The centripetal acceleration causes the object to slow down.

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC NDA-2 – 2017

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When an object moves in a circular path with constant speed $v$, it experiences a centripetal acceleration $a_c$ directed towards the center of the circle. The formula for centripetal acceleration is $a_c = \frac{v^2}{r}$, where $v$ is the speed and $r$ is the radius of the circular path. For a constant speed $v$, the centripetal acceleration is inversely proportional to the radius $r$. A gentle curve corresponds to a larger radius ($r$), while a sharp curve corresponds to a smaller radius ($r$). Therefore, for a constant speed, a larger radius (gentle curve) results in a smaller centripetal acceleration, and a smaller radius (sharp curve) results in a larger centripetal acceleration. Option A correctly states that the centripetal acceleration is smaller for a gentle curve (larger radius) than for a sharp curve (smaller radius).

– Centripetal acceleration $a_c = \frac{v^2}{r}$.
– For constant speed $v$, $a_c \propto \frac{1}{r}$.
– Gentle curve = larger radius; Sharp curve = smaller radius.

Centripetal acceleration is always perpendicular to the velocity vector in uniform circular motion and is responsible for changing the direction of velocity, thus keeping the object on the circular path, without changing its speed. Option D is incorrect because centripetal acceleration changes direction, not speed (in uniform circular motion).

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