Question

Centripetal acceleration is
A.) A constant vector
B.) A constant scalar
C.) A magnitude changing vector
D.) Not a constant vector

Answer 1

Hint: In order to deal with this question first we will define the centripetal acceleration then we will understand its formula and according to the formula we will understand whether it is a vector or scalar and also about its magnitude. We will proceed further to find the correct option.

Complete step by step answer:

Formula used- ${a_c} = \dfrac{{{v^2}}}{R}$
Centripetal acceleration is the property of the motion of a body which is moving in a circular path.
The acceleration which acts radially towards the centre of the circle and which has a magnitude equal to the square of the speed of the body along the curve divided by the total distance from the center of the circle to the moving body.
When an object is moving in a circular motion, acceleration can be measured by using the following equation-
${a_c} = \dfrac{{{v^2}}}{R}$
Where,
${a_c}$ is the centripetal acceleration
v is the velocity
R is the radius in m.
So, it is always directed towards the center of the circle.
Since velocity and radius are constants for a given uniform circular motion, so the magnitude of centripetal acceleration is also always constant.
But, the direction of centripetal acceleration changes continuously in the circular path. So, centripetal acceleration is not a constant vector.
Hence, centripetal acceleration is not a constant vector.

So, the correct answer is option D.

Note- The force that causes the acceleration of the centripetal is directed towards the center of the circle and is called centripetal. Acceleration should be expressed in meters per second, as it is the amount of meters every second that affects the velocity every second. Merry-go-rounds are a good example of how it takes momentum to hold an object going along a circular direction. When you drive a car in a circle the centripetal force is the frictional force between the ground and the tyres.