Answer:

Explanation:
It is given that,
Angular speed of the football spiral, 
Radius of a pro football, r = 8.5 cm = 0.085 m
The velocity is given by :


v = 3.68 m/s
The centripetal acceleration is given by :



So, the centripetal acceleration of the laces on the football is
. Hence, this is the required solution.
Explanation:
Th electric force between charges is inversely proportional to the square of distance between them. It means,

Initial distance, r₁ = 2 cm
Final distance, r₂ = 0.25 cm
Initial force, F₁ = 1 N
We need to find the electric force between charges if the new separation of 0.25 cm. So,

So, the new force is 64 N if the separation between charges is 64 N.
Answer:
v = 1.6 m/s
Explanation:
Given that,
Distance, d = 72 m
Time taken, t = 45 s
We need to find their average velocity. Average velocity of an object is given by total distance divided by total time taken.

So, their average velocity is 1.6 m/s.
Answer: F = mg(1 + 4m / (½M + m))
Explanation:
"At this point seems" unclear. If the particle is at the top of the disc and angular velocity is negligible, then the force would equal the weight of the particle. F = mg
The more interesting question would be what force is needed to keep the particle attached when significant angular rotation has been achieved. The maximum point would be diametrically opposed to the starting point.
I will analyze it there
The potential energy will convert to kinetic energy
mgh = ½Iω²
mg(2R) = ½(½MR² + mR²)ω²
4mgR = R²(½M + m)ω²
ω² = 4mg / (R(½M + m))
With m at the lowest position, the force of attachment must support the weight of m and provide for the needed centripetal acceleration
F = m(g + ω²R)
F = m(g + 4mg / (R(½M + m))R)
F = mg(1 + 4m / (½M + m))