The radius of the path of an object in uniform circular motion is doubled the centripetal for needed if its speed remains the same is

Centripetal force that keeps an object in circular motion. The centripetal force will reduce by half if radius is increased by two times.

The formula centripetal force that keeps an object in circular motion  

Where

m is mass of object,

v is velocity ,

r is the radius

From the formula, the Force is inversely proportional to the radius of the path.

Therefore, the centripetal force will reduce by half if radius is increased by two times.

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The centripetal force is reduced by half.

Explanation:

Now the centripetal force that keeps an object in circulation motion is given as;

F = mv^2/r

Where m is mass of object, v is velocity , r is the raduis

Looking at the formula above,

If we double r , force will reduce by 1/2 since Force is inversely proportional to the raduis of the path of the motion.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .