Answer:
Angle with the +x axis is θ = 79.599degree
Then the velocity of owner = 1.235m/s
Explanation:
Given that the mass of dog is m1 =26.2 kg
velocity of dog is u1 = 3.02 m/s (north)
mass of cat is m2 = 5.3 kg
velocity is u2 = 2.74 m/s (east )
Mass of owner is M = 65.1 kg
Consider the east direction along +x axis andnorth along +y
momentum of dog is Py = m1 x u1
= 79.124 kg.m/s (j)
momentum of cat is Px = m2 x u2
= 14.522 kg.m/s (i)
Then the net magnitude of momentum is P = (Px2 + Py2)1/2
= 80.445
Angle with the +x axis is θ =tan-1(Py / Px ) = 79.599 degree
Then the velocity of owner is v = P / M = 1.235 m/s
Answer:
proof in explanation
Explanation:
First, we will calculate the number of half-lives:

where,
n = no. of half-lives = ?
t = total time passed = 2100 million years
= half-life = 700 million years
Therefore,

Now, we will calculate the number of uranium nuclei left (
):

and the rest of the uranium nuclei will become thorium nuclei (
)

dividing both:

<u>Hence, it is proven that after 2100 million years there are seven times more thorium nuclei than uranium nuclei in the rock.</u>
The concept of power is given by the relationship between intensity and area, that is to say that power is defined as

Our values are given under the condition of,


The power is proportional to the Area, and in turn, we know that the Area of a circle is the product between
times the radius squared, therefore the power is proportional to the radius squared.

For both panels we would have to



Therefore the correct option is option C.9
Answer:

Explanation:
It is given that,
Length of the wire, L = 0.6 m
Current flowing inside the wire, I = 2 A
Uniform magnetic field, B = 0.3 T
Force experienced by the wire in the magnetic field, F = 0.18 N
To find,
The angle made by the wire with the magnetic field.
Solve,
We know that the magnetic force acting on the wire inside the magnetic field is given by :




Therefore, the wire makes an angle of 30 degrees with respect to magnetic field.
To solve this problem it is necessary to apply the kinematic equations of angular motion.
Torque from the rotational movement is defined as

where
I = Moment of inertia
For a disk
Angular acceleration
The angular acceleration at the same time can be defined as function of angular velocity and angular displacement (Without considering time) through the expression:

Where
Final and Initial Angular velocity
Angular acceleration
Angular displacement
Our values are given as






Using the expression of angular acceleration we can find the to then find the torque, that is,




With the expression of the acceleration found it is now necessary to replace it on the torque equation and the respective moment of inertia for the disk, so




Therefore the torque exerted on it is 