PHYSICS COLLEGE

A grandfather clock keeps time using a pendulum consisting of a light rod connected to a small heavy mass. With a rod of length L, the period of oscillation is 2.00 s. What should the length of the rod be for the period of the oscillations to be 1.00 s?

Answers

Answer 1
Answer:

Answer:

The length of the rod should be

(L)/(4) \n

Explanation:

Period of simple pendulum is given by

T=2\pi\sqrt{(l)/(g)} \n

We have

(T_1^2)/(T_2^2)=(l_1)/(l_2)\n\n(2^2)/(1^2)=(L)/(l_2)\n\nl_2=(L)/(4) \n

The length of the rod should be

(L)/(4) \n

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The thickness of a $1 bill is 0.11 mm. If you have a stack of $1 bills 450 m tall, how much money do you have?

Answers

Answer:

4090909

Explanation:

Thickness of one bill = 0.11 mm

Total thickness = 450 m

No of $1 bills = total thickness / thickness of one bill

No of $1 bills = 450 / 0.11 × 10^-3

= 4090909

Answer:

You will have 4.5 million dollar

Explanation:

The thickness of a $1 bill is 0.11 mm

So we have

              1 $ = 0.1 mm

              0.1 mm = 1 $

              0.0001 m =  1 $

              1 m = 10000 $

           450 m = 450 x 10000 = 4500000 $

So you will have 4.5 million dollar

The distance in the x direction between two control points on a vertical aerial photograph is 4.5". If the distance between these same two points is 3.6" on another photograph having a scale of 1:24,000, determine the scale of the first vertical aerial photograph. Of the focal length of the camera is 6"and the average elevation at these points is 100 ft, determine the flying height from which each photograph was taken

Answers

Answer:

Use proportions to find the scale of the first photo, then use that scale and other given information to fill in the equation

S=f/(H-h)

Where:

S = scale of the photo

f = focal length of the camera (in feet)

H = flying height

h = average elevation

A laser (electromagnetic wave) has the maximum electric field strength of 1.0x1011 V/m. What is the force the laser applies on a mirror (totally reflective) of 5.0 mm2 area? A. 2.76 x105N B. 1.21 x106N C. 1.94 x106N D.4.43 x105 N E. 7.82 x104N

Answers

Answer:

The correct option is  D

Explanation:

From the question we are told that

  The maximum electric field strength is  E = 1.0 *10^(11) \ V/m

   The  area is  A = 5.0 \ mm^2 = 5.0 *10^(-6) \ m^2

Generally the force the laser applies is mathematically represented as

       F = \epsilon_o * E ^2 * A

Here  \epsilon_o = 8.85*10^(-12) C/(V \cdot m)

      F = 8.85*10^(-12) * (1.0 *10^(11)) ^2 * 5.00*10^(-6 )

=>   F = 4.43 *10^(5) \ N

According to the Heisenberg uncertainty principle, quantum mechanics differs from classical mechanics in that: Select the correct answer below: Quantum mechanics involves particles that do not move. It is impossible to calculate with accuracy both the position and momentum of particles in classical mechanics. The measurement of an observable quantity in the quantum domain inherently changes the value of that quantity. All of the above

Answers

Answer:

Statement 3 is correct.

Heisenberg's uncertainty principle explains that the measurement of an observable quantity in the quantum domain inherently changes the value of that quantity

Explanation:

Classical mechanics is the study of motion of big, relatable bodies that we come in contact with in our day to day lives.

Quantum mechanics refers to this same study, but for particles on a subatomic level.

Obviously, Classical mechanics' theories and principles were first discovered and they worked for their intended uses (still work!). But when studies on particles on a sub-atomic level intensified, it became impractical to apply those theories and principles to these sub-atomic particles that displayed wave-particle duality nature properly.

Heisenberg's Uncertainty principle came in a time that explanations and justifications were needed to adapt these theories to sub-atomic particles.

The principle explains properly that it is impossible to measure the position and velocity (momentum) of a sub-atomic particle in exact terms and at the same time.

Mathematically, it is presented as

Δx.Δp ≥ ℏ

Where ℏ= adjusted Planck's constant.

ℏ= (h/2π)

And Δx and Δp are the uncertainties in measuring the position and momentum of sub-atomic particles.

The major reason for this is the wave-particle duality of sub-atomic particles. They exist as waves and particles at the same time that a complete knowledge of their position mean that a complete ignorance of their velocity and vice versa.

Taking the statements one at a time

Statement 1

Quantum Mechanics studies sub-atomic particles which are mostly always in motion. So, this is false.

Statement 2

It is impossible to calculate with accuracy both the position and momentum of particles in quantum mechanics not classical mechanics. As stated above, the reason for the uncertainty is the wave-particle duality of sub-atomic particles which the particle in classical mechanics do not exhibit obviously enough.

Statement 3

Any attempt to measure precisely the velocity of a subatomic particle, will knock it about in an unpredictable way, so that a simultaneous measurement of its position has no validity.

An essential feature of quantum mechanics is that it is generally impossible, even in principle, to measure a system without disturbing it. This is basically the uncertainty principle rephrased. This is the only true statement.

Hope this Helps!!!

An electric current in a conductor varies with time according to the expression i(t) = 110 sin (120πt), where i is in amperes and t is in seconds. what is the total charge passing a given point in the conductor from t = 0 to t = 1/180 s?

Answers

As we know that current is defined as rate of flow of charge

i = (dq)/(dt)

so by rearranging the equation we can say

q = \int i dt

here we know that

i(t) = 110 sin(120\pi t)

here we will substitute it in the above equation

q = \int 110 sin(120\pi t) dt

q = 110 [- (cos(120\pi t))/(120\pi)]

now here limits of time is from t = 0 to t = 1/180s

so here it will be given as

q = (110)/(120\pi)( -cos0 + cos((2\pi)/(3)))

q = 0.44 C

so total charge flow will be 0.44 C

Answer:

The total charge passing a given point in the conductor is 0.438 C.

Explanation:

Given that,

The expression of current is

i(t)=110\sin(120\pi t)

(dq(t))/(t)=110\sin(120\pi t)

dq(t)=110\sin(120\pi t)dt....(I)

We need to calculate the total charge

On integrating both side of equation (I)

\int_(0)^(q)dq(t)=\int_(0)^{(1)/(180)}110\sin(120\pi t)dt

q=110((-\cos(120\pi t))/(120\pi))_(0)^{(1)/(180)}

q=-(110)/(120\pi)(cos(120\pi((1)/(180)))-\cos120\pi(0))

q=-0.2918(-(1)/(2)-1)

q=0.438\ C

Hence,  The total charge passing a given point in the conductor is 0.438 C.

A wheel starts at rest, and has an angular acceleration of 4 rad/s2. through what angle does it turn in 3.0 s?

Answers

As we know from kinematics

\theta = w_o *t + (1)/(2)\alpha t^2

\theta = 0 + (1)/(2)*4*3^2

\theta = 18 radian

So it will turn by 18 radian
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