Answer:
The current flowing through the outer coils is
Explanation:
From the question we are told that
The number of turn of inner coil is 
The radius of inner coil is 
The current flowing through the inner coil is 
The number of turn of outer coil is 
The radius of outer coil is 
For net magnetic field at the common center of the two coils to be zero the current flowing in the outer coil must be opposite to current flowing inner coil
The magnetic field due to inner coils is mathematically represented as

The magnetic field due to inner coils is mathematically represented as

Now for magnetic field at center to be zero

So

=> 

Answer:
x = 1.26 sin 3.16 t
Explanation:
Assume that the general equation of the displacement given as
x = A sinω t
A=Amplitude ,t=time ,ω=natural frequency
We know that speed V

V= A ω cosωt
Maximum velocity
V(max)= Aω
Given that F= 32 N
F = K Δ
K=Spring constant
Δ = 0.4 m
32 =0.4 K
K = 80 N/m
We know that ω²m = K
8 ω² = 80
ω = 3.16 s⁻¹
Given that V(max)= Aω = 4 m/s
3.16 A = 4
A= 1.26 m
Therefore the general equation of displacement
x = 1.26 sin 3.16 t
The formula for energy of motion is KE = .5 x m x v^2
Ke= Kinetic Energy in Joules
m = Mass in Kilograms
v = Velocity in Meters per Second
The energy achieved I think
Answer:
Power= 0.5hp = 375W
T = 3hrs = 10800s
Power = Work done/ Time
Work = Power * Time = 375 * 10800 = 4050000J