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sveta [45]
2 years ago
15

Find the ratio of the lengths of the two mathematical pendulums, if the ratio of periods is 1.5​

Physics
1 answer:
juin [17]2 years ago
3 0

Answer:

The ratio of lengths of the two mathematical pendulums is 9:4.

Explanation:

It is given that,

The ratio of periods of two pendulums is 1.5

Let the lengths be L₁ and L₂.

The time period of a simple pendulum is given by :

T=2\pi \sqrt{\dfrac{l}{g}}

or

T^2=4\pi^2\dfrac{l}{g}\\\\l=\dfrac{T^2g}{4\pi^2}

Where

l is length of the pendulum

l\propto T^2

or

\dfrac{l_1}{l_2}=(\dfrac{T_1}{T_2})^2 ....(1)

ATQ,

\dfrac{T_1}{T_2}=1.5

Put in equation (1)

\dfrac{l_1}{l_2}=(1.5)^2\\\\=\dfrac{9}{4}

So, the ratio of lengths of the two mathematical pendulums is 9:4.

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A 102 kg football player runs at a speed of 8 m/s to sack the quarterback. What is
leva [86]

The mass of the quarterback is 61.2 kg.

Explanation:

mass of the football player = m1 = 102 kg

mass of the quarterback = m2 = ?

velocity of the football player = v1 = 8 m/s

According to the law of conservation of momentum:

The total momentum of a system before and after the collision remains constant. Assuming the situation as an isolated system which is not affected by any external factors, we have:

m₁v₁ + m₂v₂ = (m₁+m₂)V

Here, we need to find m₂.

We assume that the quarterback is standing still when he is attacked by the football player so v₂ = 0 m/s

After the collision both of them fall to the ground with a velocity of 5 m/s so V = 5 m/s

102(8) + m2(0) = (102 + m2)(5)\\816 + 0 = (102 + m2)(5)\\816/5 = 102 + m2\\163.2 - 102 = m2\\m2 = 61.2 kg

Keywords: momentum, velocity, law of conservation of momentum

Learn more about Law of Conservation of Momentum from brainly.com/question/7538238

#learnwithBrainly

3 0
3 years ago
What is the great red spot? what is the great red spot? a long-lived, high-pressure storm on jupiter a place where reddish parti
maxonik [38]
<span><u><em>A</em></u><em><u></u></em><em><u></u></em><u><em> long-lived, high-pressure storm on jupiter a place where reddish particles from io impact jupiter's surface</em></u></span><u><em> </em></u>
5 0
2 years ago
There are 5510 lines per centimeter in a grating that is used with light whose wavelegth is 467 nm. A flat observation screen is
Mademuasel [1]

Answer:

1.696 nm

Explanation:

For a diffraction grating, dsinθ = mλ where d = number of lines per metre of grating = 5510 lines per cm = 551000 lines per metre and λ = wavelength of light = 467 nm = 467 × 10⁻⁹ m. For a principal maximum, m = 1. So,

dsinθ = mλ = (1)λ = λ

dsinθ = λ

sinθ = λ/d.

Also tanθ = w/D where w = distance of center of screen to principal maximum and D = distance of grating to screen = 1.03 m

From trig ratios 1 + cot²θ = cosec²θ

1 + (1/tan²θ) = 1/(sin²θ)

substituting the values of sinθ and tanθ we have

1 + (D/w)² = (d/λ)²

(D/w)² = (d/λ)² - 1

(w/D)² = 1/[(d/λ)² - 1]

(w/D) = 1/√[(d/λ)² - 1]

w = D/√[(d/λ)² - 1] = 1.03 m/√[(551000/467 × 10⁻⁹ )² - 1] = 1.03 m/√[(1179.87 × 10⁹ )² - 1] = 1.03 m/1179.87 × 10⁹  = 0.000848 × 10⁻⁹ = 0.848 × 10⁻¹² m = 0.848 nm.

w is also the distance from the center to the other principal maximum on the other side.

So for both principal maxima to be on the screen, its minimum width must be 2w = 2 × 0.848 nm = 1.696 nm

So, the minimum width of the screen must be 1.696 nm

4 0
3 years ago
A sample of argon gas (molar mass 40 g) is at four times the absolute temperature of a sample of hydrogen gas (molar mass 2 g).
qaws [65]

To solve this problem, let us recall that the formula for gases assuming ideal behaviour is given as:

rms = sqrt (3 R T / M)

where

R = gas constant = 8.314 Pa m^3 / mol K

T = temperature

M = molar mass

Now we get the ratios of rms of Argon (1) to hydrogen (2):

rms1 / rms2 = sqrt (3 R T1 / M1) / sqrt (3 R T2 / M2)

or

rms1 / rms2 = sqrt ((T1 / M1) / (T2 / M2))

rms1 / rms2 = sqrt (T1 M2 / T2 M1)

Since T1 = 4 T2

rms1 / rms2 = sqrt (4 T2 M2 / T2 M1)

rms1 / rms2 = sqrt (4 M2 / M1)

and M2 = 2 while M1 = 40

rms1 / rms2 = sqrt (4 * 2 / 40)

rms1 / rms2 = 0.447

 

Therefore the ratio of rms is:

<span>rms_Argon / rms_Hydrogen = 0.45</span>

7 0
3 years ago
Please help me with this question...
vredina [299]
The answer is B (The second one). I'm not sure though.
3 0
3 years ago
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