What si unit measures speed ?

A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axi

Lubov Fominskaja [6]

Answer:

The moment of inertia is $I=\frac{M}{12} a^{2}$

Explanation:

The moment of inertia is equal:

$I=\int\limits^a_b {r^{2} } \, dm$

If r is $-\frac{a}{2}$

and $dm=\frac{M}{a} dr$

$I=\int\limits^a_b {r^{2}\frac{M}{a} } \, dr\\a=\frac{a}{2} \\b=-\frac{a}{2}$

$I=\frac{M}{a} \int\limits^a_b {r^{2} } \, dr\\\\I=\frac{M}{a} (\frac{M}{3} )_{b}^{a}\\ I=\frac{M}{3a} (\frac{a^{3} }{8} +\frac{a^{3} }{8} )\\I=\frac{M}{12} a^{2}$

7 0

3 years ago

What is the effect on the force of gravity between two objects if the mass of one object remains unchanged while the distance to

Vadim26 [7]

Answer:

The correct answer to the question is

B. It always decreases

Explanation:

To solve the question, we note that the foce of gravity is given by

$F_G=\frac{Gm_1m_2}{r^2}$ where

G= Gravitational constant

m₁ = mass of first object

m₂ = mass of second object

r = the distance between both objects

If the mass of one object remains unchanged while the distance to the second object and the second object’s mass are both doubled, we have

$F_{G2} =\frac{Gm_1(2m_2)}{(2r)^2}$ = $\frac{2}{4} \frac{Gm_1m_2}{r^2}$

Therefore the gravitational force is halved. That is it will always decrease

4 0

2 years ago

You toss a ball straight up with an initial speed of 30m/s. How high does it go, and how long is it in the air (neglecting air r

Brut [27]

Explanation:

Given that,

A ball is tossed straight up with an initial speed of 30 m/s

We need to find the height it will go and the time it takes in the air.

At its maximum height, its final speed, v = 0 and it will move under the action of gravity. Using equation of motion :

v = u +at

Here, a = -g

v = u -gt

i.e. u = gt

$t=\dfrac{u}{g}\\\\t=\dfrac{30\ m/s}{9.8\ m/s^2}\\\\t=3.06\ s$

So, the time for upward motion is 3.06 seconds. It means that it will in air for 3.06×2 = 6.12 seconds

Let d is the maximum distance covered by it.

$d=ut-\dfrac{1}{2}gt^2$

Putting all values

$d=30(3.06)-\dfrac{1}{2}\times 9.8\times (3.06)^2\\\\d=45.91\ m$

Hence, it will go to a height of 45.91 m and it will in the air for 6.12 seconds.

8 0

2 years ago

Which best describes a major characteristic of both volcanoes and earthquakes? they are centered at the poles?

Arturiano [62]

<span>A major characteristic of both volcanoes and earthquakes is that they are located in the same geographic area. Most earthquakes are along the edges of tectonic plates. This is where most volcanoes are too. Most earthquakes directly beneath a volcano are caused by the movement of magma.</span>

6 0

2 years ago

Because P and S waves travel faster through the Earth's mantle than through Earth's crust, scientists know that the mantle is __

larisa [96]

B. liquid and less denser

6 0

2 years ago

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