Give two examples of gravity in the solar system

Consider two uniform solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger mom

Firdavs [7]

Answer:

The ratio of moment of inertia of larger sphere to that of smaller sphere = 4

Explanation:

The moment of inertia of solid sphere is given by I = 2/5MR² where M = mass of sphere and R = radius of sphere.

Radius of smaller sphere = D/2

Radius of larger sphere = 2D/2 = D.

Moment of inertia of smaller sphere I₁ = 2/5M × D²/4 = MD²/10

Moment of inertia of larger sphere I₂ = 2/5M × D² = 2MD²/5

The ratio of moment of inertia of larger sphere to that of smaller sphere = I₂/I₁ = 2MD²/5 ÷ MD²/10 = 10 × 2/5 = 4

7 0

3 years ago

IMPORTANT 3 QUESTIONS!

Brums [2.3K]

Answer:

7. 20,000,000 mL.

8. 8,000 m.

9. 120,000 secs.

10. 4

Explanation:

7. Determination of the volume in millilitres (mL)

Volume in litre (L) = 20,000 L

Volume in millilitres (mL) =..?

The volume in mL can be obtained as follow:

1 L = 1,000 mL

Therefore,

20,000 L = 20,000 x 1,000 = 20,000,000 mL.

Therefore, 20,000 L is equivalent to 20,000,000 mL.

8. Determination of the distance in metre (m)

Distance in mile = 5 mile

Distance in metre =?

First, we shall convert from mile to kilometre.

This can be done as follow:

1 mile = 1.6 km

Therefore,

5 mile = 5 x 1.6 = 8 km

Finally, we shall convert 8 km to metre (m).

This is illustrated below:

1 km = 1,000 m

Therefore,

8 km = 8 x 1,000 = 8,000 m

Therefore, 5 miles is equivalent to 8,000 m.

9. Determination of the time in seconds.

Time = 400 minutes for 5 days.

First, we shall convert 400 mins to hour.

This is illustrated below:

60 minutes = 1 hour

Therefore,

400 mins = 400/60 = 20/3 hours

The time (hours) is 20/3 hours in 1 day.

Therefore, the time (hours) in 5 days will be = 20/3 x 5 = 100/3 hours.

Next, we shall convert 100/3 hours to minutes.

This is illustrated below:

1 hour = 60 minutes

Therefore,

100/3 hours = 100/3 x 60 = 2000 mins

Finally, we shall convert 2000 mins to seconds.

This is illustrated below:

1 mins = 60 secs

2000 mins = 2000 x 60 = 120,000 secs.

Therefore, the time is 120,000 secs.

10. Determination of the number of significant figures.

To obtain the significant figures of a number, we simply count all the numbers available.

Therefore, the number of significant figures for 9876 is 4.

6 0

4 years ago

A hand pump is being used to inflate a bicycle tire that has a gauge pressure of 59.0 lb/in2. If the pump is a cylinder of lengt

bagirrra123 [75]

Answer:

∴The air cannot be made to flow in with the given pump at the given conditions.

Explanation:

Given:

gauge pressure of bicycle tyre, $P_g=59\ lb.in^{-2}$

length of cylinder of the pump, $l=17.4\ in$

area of the the cylinder of the pump, $a= 3\ in^2$

we have the density of air at STP, $\rho=4.4256\times 10^{-5}\ lb.in^{-2}$

The piston must be pushed more than the pressure inside the tyre:

$P_g=\rho\times V\div a$

$59=4.4256\times 10^{-5}\times a\times h\div a$

$h=13.33\times 10^5\ in$

∴The air cannot be made to flow in with the given pump at the given conditions.

4 0

3 years ago

Wonder Woman and Superman fly to an altitude of 1690 km , carrying between them a chest full of jewels that they intend to put i

Arturiano [62]

Answer:

5120 m/s

Explanation:

The acceleration due to gravity is:

g = MG / r²

where M is the mass of the earth, G is the universal constant of gravitation, and r is the distance from the earth's center to the object's center.

Here, r = h + R, where h is the height of the chest above the surface and R is the radius of the earth.

g = MG / (h + R)²

Acceleration is the derivative of velocity:

dv/dt = MG / (h + R)²

Using chain rule, we can say:

(dv/dh) (dh/dt) = MG / (h + R)²

(dv/dh) v = MG / (h + R)²

Separate the variables:

v dv = MG / (h + R)² dh

Integrating:

∫₀ᵛ v dv = MG ∫₀ʰ dh / (h + R)²

½ v² |₀ᵛ = -MG / (h + R) |₀ʰ

½ (v² − 0²) = -MG / (h + R) − -MG / (0 + R)

½ v² = -MG / (h + R) + MG / R

½ v² = MGh / (R(h + R))

v² = 2MGh / (R(h + R))

Given:

M = 5.98×10²⁴ kg

R = 6.37×10⁶ m

h = 1.69×10⁶ m

G = 6.67×10⁻¹¹ m³/kg/s²

Plugging in:

v² = 2 (5.98×10²⁴) (6.67×10⁻¹¹) (1.69×10⁶) / ((6.37×10⁶) (1.69×10⁶ + 6.37×10⁶))

v² = 2 (5.98) (6.67) (1.69) / ((6.37) (1.69 + 6.37)) × 10⁷

v ≈ 5120 m/s

Notice that if we had approximated g as a constant 9.8 m/s², we would have gotten an answer of:

v² = v₀² + 2a(x - x₀)

v² = (0 m/s)² + 2 (9.8 m/s²) (1.69×10⁶ m - 0 m)

v ≈ 5760 m/s

So we know that our calculated velocity of 5120 m/s is a reasonable answer.

3 0

3 years ago

A roller coaster needs to climb a tall hill. How tall of a hill can it climb with an initial

iren [92.7K]

Answer:

h = 11.25m

Explanation:

mgh = 1/2mv2

gh = 1/2v2

10 x h = 1/2 x 15 x 15

20 x h = 225

h = 225/20

h = 11.25m

3 0

4 years ago