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lina2011 [118]
2 years ago
14

If we double the diameter of a telescope's mirror, what happens to its light-gathering ability? View Available Hint(s) If we dou

ble the diameter of a telescope's mirror, what happens to its light-gathering ability?
Light-gathering ability doubles as well.
Light-gathering ability quadruples.
There is no change.
The light-gathering ability is cut in half.
Physics
1 answer:
crimeas [40]2 years ago
7 0

Answer:

Light-gathering ability quadruples.

Explanation:

The light-gathering ability of a telescope depends on the area of the mirror, which is the surface presented to the light. Since these mirrors are circular (diameter is mentioned), we need to know what happens with the area of it when its diameter is doubled.

If r is the radius and d the diameter of a circle, its area will be:

A=\pi r^2=\pi (\frac{d}{2} )^2=\pi(\frac{d^2}{4})=\frac{\pi d^2}{4}

We want to know now what happens if we double the diameter to 2d, so we calculate the new area A':

A'=\frac {\pi (2d)^2}{4}=\frac {\pi 4d^2}{4}=\pi d^2

Which is 4 times greater than the original area A, so we conclude that its light-gathering ability quadruples.

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A purse at radius 2.30 m and a wallet at radius 3.45 m travel in uniform circular motion on the floor of a merry-go-round as the
ivolga24 [154]

Answer:

The acceleration of the wallet is 3\hat{i}+6\hat{j}

Explanation:

Given that,

Radius of purse r= 2.30 m

Radius of wallet r'= 3.45 m

Acceleration of the purse a=2\hat{i}+4.00\hat{j}

We need to calculate the acceleration of the wallet

Using formula of acceleration

a=r\omega^2

Both the purse and wallet have same angular velocity

\omega=\omega'

\sqrt{\dfrac{a}{r}}=\sqrt{\dfrac{a'}{r'}}

\dfrac{a}{r}=\dfrac{a'}{r'}

\dfrac{a'}{a}=\dfrac{r'}{r}

\dfrac{a'}{a}=\dfrac{3.45}{2.30}

\dfrac{a'}{a}=\dfrac{3}{2}

a'=\dfrac{3}{2}\times(2\hat{i}+4.00\hat{j})

a'=3\hat{i}+6\hat{j}

Hence, The acceleration of the wallet is 3\hat{i}+6\hat{j}

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Is it true that playing badmenton help you to become a better person?
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Answer:

There is no scientific evidence that playing specifically l badminton makes you a better person, but sport and exercise in general release hormones which can make you feel more happy therefore making you nicer to the people around you and 'a better person'.

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As an interstellar cloud of hydrogen gas shrinks in size, its rate of rotation
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Answer:

INCREASES, BECAUSE ITS ANGULAR MOMENTUM IS CONSERVED.

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List of three questions that you are good at science questions.
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One end of a 34-m unstretchable rope is tied to a tree; the other end is tied to a car stuck in the mud. The motorist pulls side
anyanavicka [17]

Answer:

Fc = 89.67N

Explanation:

Since the rope is unstretchable, the total length will always be 34m.

From the attached diagram, you can see that we can calculate the new separation distance from the tree and the stucked car H as follows:

L1+L2=34m

L1^2=L2^2=L^2=2^2+(H/2)^2  Replacing this value in the previous equation:

\sqrt{2^2+H^2/4}+ \sqrt{2^2+H^2/4}=34  Solving for H:

H=\sqrt{52}

We can now, calculate the angle between L1 and the 2m segment:

\alpha = atan(\frac{H/2}{2})=60.98°

If we make a sum of forces in the midpoint of the rope we get:

-2*T*cos(\alpha ) + F = 0  where T is the tension on the rope and F is the exerted force of 87N.

Solving for T, we get the tension on the rope which is equal to the force exerted on the car:

T=Fc=\frac{F}{2*cos(\alpha) } = 89.67N

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3 years ago
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