Question

An object moves at uniform speed (v) in a circular path, the

centripetal acceleration is a, if the object moves in the same
circular path at uniform speed (4v) the centripetal accelera on will
be?

Answer 1

Answer: V 2 /r

Explanation: "If a particles move with a uniform speed of V on any given circular path having the radius (r), the particle will have a centripetal acceleration of magnitude (v 2 /r). However, the direction continuously changes and always maintains its position towards the circle."

Answer 2

The centripetal acceleration (a) of an object moving in a circular path is given by the formula:

a = v^2 / r

where v is the speed of the object and r is the radius of the circular path.

If the object moves at a uniform speed of 4v instead, we can plug this value into the formula to find the new centripetal acceleration (a'):

a' = (4v)^2 / r

Simplifying the expression, we get:

a' = 16v^2 / r

Now, we can compare the new centripetal acceleration (a') to the original centripetal acceleration (a):

a' = 16(a)

So, if the object moves in the same circular path at a uniform speed of 4v, the centripetal acceleration will be 16 times greater than the original centripetal acceleration.