Answer:
The tension increases by a factor of 8
Explanation:
We know that the tension, T in the string equals the centripetal force on the ball. So
T = mrω² = mr(2πf)² = 4mrπ²f² where m = mass of ball, r = radius of circle and f = frequency of rotation
If the radius and frequency are doubled, then r = 2r and f = 2f. So, the new tension is T' = 4mr'π²f'² = 4m(2r)π²(2f)² = 4 × 2 × 4mrπ²f² = 8T
Since T' = 8T,
So T'/T = 8.
So the tension increases by a factor of 8
The volume of water in the larger balloon is 8 times greater than in the smaller balloon
We'll begin by calculating the volume of each balloon.
<h3>For smaller balloon:</h3>
- Radius (r) = 3 cm
- Pi (π) = 3.14
- Volume (V) =?
V = 4/3 πr³
V = 4/3 × 3.14 × 3³
<h3>V = 113.04 cm³</h3>
<h3>For larger balloon:</h3>
- Radius (r) = 6 cm
- Pi (π) = 3.14
- Volume (V) =?
V = 4/3 πr³
V = 4/3 × 3.14 × 6³
<h3>V = 904.32 cm³</h3>
Finally, we shall determine how much greater the larger balloon is to the smaller balloon
- Volume of smaller balloon = 113.04 cm³
- Volume of larger balloon = 904.32 cm³
- Greatness =?
Greatness => large / small
Large / small = 904.32 / 113.04
Large / small = 8
Cross multiply
<h3>Large = 8 × small </h3>
Therefore, the larger balloon is 8 times greater than the smaller balloon.
Learn more on volume of sphere: brainly.com/question/9178703
Answer:


Explanation:
Given:
- mass of the object,

- elastic constant of the connected spring,

- coefficient of static friction between the object and the surface,

(a)
Let x be the maximum distance of stretch without moving the mass.
<em>The spring can be stretched up to the limiting frictional force 'f' till the body is stationary.</em>


where:
N = m.g = the normal reaction force acting on the body under steady state.


(b)
Now, according to the question:
- Amplitude of oscillation,

- coefficient of kinetic friction between the object and the surface,

Let d be the total distance the object travels before stopping.
<em>Now, the energy stored in the spring due to vibration of amplitude:</em>

<u><em>This energy will be equal to the work done by the kinetic friction to stop it.</em></u>




<em>is the total distance does it travel before stopping.</em>
You said T = 2 · π · √(L / g)
(I think that's the formula for the full-swing period of a simple pendulum.)
Divide each side by 2π : T/2π = √(L / g)
Square each side: (T/2π)² = L / g
Multiply each side by ' g ' : L = g · (T/2π)²