Answer:
The induced current is 
Explanation:
From the question we are told that
The number of turns is
The cross-sectional area is 
The initial magnetic field is 
The magnetic field at time = 1.02 s is 
The resistance is 
The induced emf is mathematically represented as

The negative sign tells us that the induced emf is moving opposite to the change in magnetic flux
Here
is the change in magnetic flux which is mathematically represented as

Where dB is the change in magnetic field which is mathematically represented as

substituting values


Thus


So


The induced current i mathematically represented as

substituting values


Answer:
a) The magnitude of the magnetic field = 7.1 mT
b) The direction of the magnetic field is the +z direction.
Explanation:
The force, F on a current carrying wire of current I, and length, L, that passes through a magnetic field B at an angle θ to the flow of current is given by
F = (B)(I)(L) sin θ
F/L = (B)(I) sin θ
For this question,
(F/L) = 0.113 N/m
B = ?
I = 16.0 A
θ = 90°
0.113 = B × 16 × sin 90°
B = 0.113/16 = 0.0071 T = 7.1 mT
b) The direction of the magnetic field will be found using the right hand rule.
The right hand rule uses the first three fingers on the right hand (the thumb, the pointing finger and the middle finger) and it predicts correctly that for current carrying wires, the thumb is in the direction the wire is pushed (direction of the force; -y direction), the pointing finger is in the direction the current is flowing (+x direction), and the middle finger is in the direction of the magnetic field (hence, +z direction).
Answer: 
Explanation:
The equation to calculate the center of mass
of a particle system is:

In this case we can arrange for one dimension, assuming the geometric center of the Earth and the ladder are on a line, and assuming original center of mass located at the Earth's geometric center:

Where:
is the mass of the Earth
is the mass of 1 billion people
is the radius of the Earth
is the distance between the center of the Earth and the position of the people (2 m above the Earth's surface)

This is the displacement of Earth's center of mass from the original center.
Answer:
19.62 ms
Explanation:
t = Time taken = 2 s
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.81 m/s² (downward direction is taken as positive)
Equation of motion

The speed of the pebble when it hit the water is 19.62 ms