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Agata [3.3K]
3 years ago
7

The specific gravity of a substance is given by G = DS/DW, where DS is the density of the substance in kg/m3 and DW is the densit

y of water, which is known to be 1000 kg/m3. The density of a particular substance is measured to be DS = 500±5 kg/m3. Estimate the specific gravity, and find the uncertainty in the estimate
Physics
1 answer:
katen-ka-za [31]3 years ago
3 0

Answer:

G=0.5\pm0.005

Explanation:

The specific gravity is given by,

G=\frac{D_S}{D_W}=\frac{500}{1000} =0.5

Now, in order to calculate the uncertainty (relative error) in G, we must first take log (base e) on both sides of the equation,

lnG=ln(\frac{D_S}{D_W} )=lnD_S-lnD_W

Differentiating the above equation,

\frac{dG}{G}=\frac{dD_S}{D_S}

The second term is zero because it is known that D_W=1000kg/m^3 and hence a constant.

Putting the appropriate values, we get,

\frac{dG}{G}=\frac{dD_S}{D_S}=\frac{5}{500} =0.01

Therefore, uncertainty in G = 0.01\times0.5=0.005

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Answer:

c. Moon A is four times as massive as moon B

Explanation:

Let's assume the:

  • mass of the object = m\,kilogram
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  • distance between the center of masses of the object and moon B = r\,meters

According to the given condition the object is twice as far from moon A as it is from moon B

  • ∴distance between the center of masses of the object and moon B = 2r\,meters

<u>As we know, gravitational force of attraction is given by:</u>

F=G\frac{m_1.m_2}{r^2}

<em>According to the condition</em>

Force on m due toM_B=Force on m due toM_A

G\frac{m.M_A}{(2r)^2} =G\frac{m.M_B}{(r)^2}

\frac{M_A}{4r^2} =\frac{M_B}{r^2}

M_A=4M_B

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3 years ago
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If a transmission line in a cold climate collects ice, the increased diameter tends to cause vortex formation in a passing wind.
AleksAgata [21]

Answer:

a) f_1=5.587Hz

b) f_{n+1}-f_n=5.587Hz

Explanation:

The frequency of the n^{th} harmonic of a vibrating string of length <em>L, </em>linear density \mu under a tension <em>T</em> is given by the formula:

f_n=\frac{n}{2L} \sqrt{\frac{T}{\mu}

a) So for the <em>fundamental mode</em> (n=1) we have, substituting our values:

f_1=\frac{1}{2(347m)} \sqrt{\frac{65.4\times10^6N}{4.35kg/m}}=5.587Hz

b) The <em>frequency difference</em> between successive modes is the fundamental frequency, since:

f_{n+1}-f_n=\frac{n+1}{2L} \sqrt{\frac{T}{\mu}}-\frac{n}{2L} \sqrt{\frac{T}{\mu}}=(n+1-n)\frac{1}{2L} \sqrt{\frac{T}{\mu}}=\frac{n}{2L} \sqrt{\frac{T}{\mu}}=f_1=5.587Hz

3 0
3 years ago
True or False? 13. All living things are made of cells 14. All cells have DNA within their nucleus 15. The cell is the basic uni
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Answer:

1: True

2: False

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3 0
2 years ago
The eyes of some reptiles are sensitive to 850 nm light. If the minimum energy to trigger the receptor at this wavelength is 3.1
mr_godi [17]

Answer:

Minimum number of photons required is 1.35 x 10⁵

Explanation:

Given:

Wavelength of the light, λ = 850 nm = 850 x 10⁻⁹ m

Energy of one photon is given by the relation :

E=\frac{hc}{\lambda}    ....(1)

Here h is Planck's constant and c is speed of light.

Let N be the minimum number of photons needed for triggering receptor.

Minimum energy required for triggering receptor, E₁ = 3.15 x 10⁻¹⁴ J

According to the problem, energy of N number of photons is equal to the energy required for triggering, that is,

E₁ = N x E

Put equation (1) in the above equation.

E_{1}=N\times\frac{hc}{\lambda}

Substitute 3.15 x 10⁻¹⁴ J for E₁, 850 x 10⁻⁹ m for λ, 6.6 x 10⁻³⁴ J s for h and 3 x 10⁸ m/s for c in the above equation.

3.15\times10^{-14} =N\times\frac{6.6\times10^{-34}\times3\times10^{8}}{850\times10^{-9}}

N = 1.35 x 10⁵

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3 years ago
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