Answer:

Explanation:
From the question we are told that
The number of turns is 
The radius is 
The position from the center consider is x = 3.45 cm = 0.0345 m
The induced emf is 
Generally according to Gauss law

=> 
Where A is the cross-sectional area of the solenoid which is mathematically represented as

=> 
=>
ggl;
Here
is the permeability of free space with value

=> 
=> 
Answer: a) B = 6811N
b) m = 603.2kg
c) 86.8%
Explanation: <em>Buoyant force</em> is a force a fluid exerts on a submerged object.
It can be calculated as:

where:
is density of the fluid the object is in;
is volume of the object;
g is acceleration due to gravity, is constant and equals 9.8m/s²
a) For the hollow plastic sphere, density of water is 1000kg/m³:

B = 6811N
b) Anchored to the bottom, the forces acting on the sphere are <u>Buoyant</u>, <u>Tension</u> and <u>Force due to gravity</u>:
B = T + 
B = T + mg
mg = B - T

Calculating:

m = 603.2kg
c) When the shpere comes to rest on the surface of the water, there are only <u>buoyant</u> <u>and</u> <u>gravity</u> acting on it:
B = m.g



= 0.6032m³
Fraction of the submerged volume is:
=
= 0.868
<u />
m = mass of the birdcage = 22.5 kg
F = net force acting on birdcage to move it = 140 N
a = acceleration produced due to the force applied
a)
Using newton's second law
a = F/m
inserting the values
a = 140/22.5
a = 6.22 m/s²
b)
t = time of travel of crate = 10.5 s
v₀ = initial velocity of the crate = 0 m/s
X = displacement of the crate
displacement of the crate is given as
X = v₀ t + (0.5) a t²
X = 0 (10.5) + (0.5) (6.22) (10.5)²
X = 342.88 m
20c because te mass of the object is larger than the table