Answer:
Mutual inductance, 
Explanation:
(a) A toroidal solenoid with mean radius r and cross-sectional area A is wound uniformly with N₁ turns. A second thyroidal solenoid with N₂ turns is wound uniformly on top of the first, so that the two solenoids have the same cross-sectional area and mean radius.
Mutual inductance is given by :

(b) It is given that,


Radius, r = 10.6 cm = 0.106 m
Area of toroid, 
Mutual inductance, 

or

So, the value of mutual inductance of the toroidal solenoid is
. Hence, this is the required solution.
Directly proportional to pressure
I attached the missing picture.
The force of seat acting on the child is a reaction the force of child pressing down on the seat. This is the third Newton's law. The force of a child pressing down the seat and the force of the seat pushing up on the child are the same.
There two forces acting on the child. The first one is the gravitational force and the second one is centrifugal force. In this example, the force of gravity is always pulling down, but centrifugal force always acts away from the center of circular motion.
Part AFor point A we have:

In this case, the forces are aligned, centrifugal is pointing up and gravitational is pulling down.
Part BAt the point, B situation is a bit more complicated. In this case force of gravity and centrifugal force are not aligned. We have to look at y components of this forces, y-axis, in this case, is just pointing upward.
Part CThe child will stay in place at point A when centrifugal force and force of gravity are in balance:
Answer:

Explanation:
= Length of wire = 65 m
= Initial current = 1.8 A
= Final current = 2.9 A
We know

and


so

The length of the wire remaining on the spool is
.
Answer:
v = 2 v₁ v₂ / (v₁ + v₂)
Explanation:
The body travels the first half of the distance with velocity v₁. The time it takes is:
t₁ = (d/2) / v₁
t₁ = d / (2v₁)
Similarly, the body travels the second half with velocity v₂, so the time is:
t₂ = (d/2) / v₂
t₂ = d / (2v₂)
The average velocity is the total displacement over total time:
v = d / t
v = d / (t₁ + t₂)
v = d / (d / (2v₁) + d / (2v₂))
v = d / (d/2 (1/v₁ + 1/v₂))
v = 2 / (1/v₁ + 1/v₂)
v = 2 / ((v₁ + v₂) / (v₁ v₂))
v = 2 v₁ v₂ / (v₁ + v₂)