Question

A ball is whirled on the end of a string in a horizontal circle of radius R at constant speed v. Complete the following statement: The centripetal acceleration of the ball can be increased by a factor of 4 by Entry field with incorrect answer keeping the radius fixed and increasing the period by a factor of 4. keeping the radius fixed and increasing the speed by a factor of 4. keeping the radius fixed and decreasing the period by a factor of 4. keeping the speed fixed and decreasing the radius by a factor of 4. keeping the speed fixed and increasing the radius by a factor of 4.

Answer 1

Answer:

Keeping the speed fixed and decreasing the radius by a factor of 4

Explanation:

A ball is whirled on the end of a string in a horizontal circle of radius R at constant speed v. The centripetal acceleration is given by :

$a=\dfrac{v^2}{R}$

We need to find how the "centripetal acceleration of the ball can be increased by a factor of 4"

It can be done by keeping the speed fixed and decreasing the radius by a factor of 4 such that,

R' = R/4

New centripetal acceleration will be,

$a'=\dfrac{v^2}{R'}$

$a'=\dfrac{v^2}{R/4}$

$a'=4\times \dfrac{v^2}{R}$

$a'=4\times a$

So, the centripetal acceleration of the ball can be increased by a factor of 4.

Answer 2

The centripetal acceleration of the ball can be increased by a factor of 4 by keeping the speed fixed and decreasing the radius by a factor of 4.

What is Centripetal acceleration?

Centripetal acceleration is the inward acceleration of an object moving in a circular path. The magnitude of centripetal acceleration can be obtained using the following formulas;

a = v²/r

where;

• v is the speed
• r is the radius of the circular path

When the speed is constant, centripetal acceleration can be increased by reducing the radius of the circle.

v² = ar

a₁r₁ = a₂r₂

r₂ = a₁r₁/a₂

when the acceleration is increased by a factor of 4

r₂ = (a₁r₁)/(4a₁)

r₂ = r₁/4

Thus, the centripetal acceleration of the ball can be increased by a factor of 4 by keeping the speed fixed and decreasing the radius by a factor of 4.

Learn more about centripetal acceleration here: https://brainly.com/question/79801