Answer:
The charge on the dust particle is 
Explanation:
From the question we are told that
The length is 
The width is 
The charge is 
The mass suspended in mid-air is 
Generally the electric field on the carpet is mathematically represented as
Where 
is the permittivity of free space with value 
substituting values
Generally the electric force keeping the dust particle on the air equal to the force of gravity acting on the particles
=> 
=> 
=> 
=>
Answer:
Explanation:
The period of a simple pendulum is given by:
where
L is the length of the pendulum
g is the acceleration of gravity
From this equation we can write
Taking the square of this equation, we get:
So we see that 
is proportional to L and inversely proportional to g. So, we can write:
So the only correct option is
Answer:
You will hear the note E₆
Explanation:
We know that:
Your speed = 88m/s
Original frequency = 1,046 Hz
Sound speed = 340 m/s
The Doppler effect says that:
Where:
f = original frequency
f' = new frequency
v = velocity of the sound wave
v0 = your velocity
vs = velocity of the source, in this case, the source is the diva, we assume that she does not move, so vs = 0.
Replacing the values that we know in the equation we have:
This frequency is close to the note E₆ (1,318.5 Hz)
Answer:
1/2 m v^2 + 1/2 I ω^2 = m g h conservation of energy
I = 2/5 m R^2 inertia of solid sphere
1/2 m v^2 + 1/5 m ω^2 R^2 = m g h
1/2 v^2 + 1/5 v^2 = g h
v^2 = 10 g h / 7 = 1.43 * 9.80 * 19 m^2/s^2 = 266 m^2/s^2
v = 16.3 m/s
v = R ω
ω = 16.3 / .6 = 27.2 / sec
