Answer:
The current in the solenoid=0.463 Ampere
Explanation:
Given:
Number of turns , N=420
Length of the solenoid=0.575 m
Magnitude of Magnetic Field,
We know that the magnitude of the magnetic Field inside the solenoid is

Where
is the permeability of free space.- n is the number of turns per unit length
- i is the current
According to question

Hence the current is calculated.
This question involves the concept of the scalar product.
The magnitude of the scalar product will be "0".
<h3>SCALAR PRODUCT</h3>
The scalar product, also known as the dot product of the two vectors is given by the following formula:

where,
- A.B = Scalar product = ?
- |A| = Mangnitude of vector A = 1 unit
- |B| = Magnitude of Vector B = 1 unit
- θ = Angle between vectors = 90°
Therefore,

A.B = 0
Learn more about scalar product here:
brainly.com/question/6849226
Answer:12.8 ft/s
Explanation:
Given
Speed of hoop 
height of top 
Initial energy at bottom is

Where m=mass of hoop
I=moment of inertia of hoop
=angular velocity
for pure rolling 



Energy required to reach at top


Thus 512.2 m is converted energy is spent to raise the potential energy of hoop and remaining is in the form of kinetic and rotational energy

Therefore



It has to be the right answer for it to be correct