Answer:
200 N
Explanation:
Since Young's modulus for the metal, E = σ/ε where σ = stress = F/A where F = force on metal and A = cross-sectional area, and ε = strain = e/L where e = extension of metal = change in length and L = length of metal wire.
So, E = σ/ε = FL/eA
Now, since at break extension = e.
So making e subject of the formula, we have
e = FL/EA = FL/Eπr² where r = radius of metal wire
Now, when the radius and length are doubled, we have our extension as e' = F'L'/Eπr'² where F' = new force on metal wire, L' = new length = 2L and r' = new radius = 2r
So, e' = F'(2L)/Eπ(2r)²
e' = 2F'L/4Eπr²
e' = F'L/2Eπr²
Since at breakage, both extensions are the same, e = e'
So, FL/Eπr² = F'L/2Eπr²
F = F'/2
F' = 2F
Since F = 100 N,
F' = 2 × 100 N = 200 N
So, If the radius and length of the wire were both doubled then it would break when the tension reached 200 Newtons.
Answer:
a.
b. 
Explanation:
<u>Given:</u>
- Velocity of the particle, v(t) = 3 cos(mt) = 3 cos (0.5t) .
<h2>
(a):</h2>
The acceleration of the particle at a time is defined as the rate of change of velocity of the particle at that time.
At time t = 3 seconds,
<u>Note</u>:<em> The arguments of the sine is calculated in unit of radian and not in degree.</em>
<h2>
(b):</h2>
The velocity of the particle at some is defined as the rate of change of the position of the particle.
For the time interval of 2 seconds,
The term of the left is the displacement of the particle in time interval of 2 seconds, therefore,
It is the displacement of the particle in 2 seconds.
Answer:
Explanation:
mass of 1 L water = 1 kg .
200⁰F = (200 - 32) x 5 / 9 = 93.33⁰C .
260.928 K = 260.928 - 273 = - 12.072⁰C .
water is at higher temperature .
Let the equilibrium temperature be t .
Heat lost by water = mass x specific heat x fall of temperature
= 1 x 4.2 x 10³ x ( 93.33 - t )
Heat gained by copper
= .25 x .385 x 10³ x ( t + 12.072 )
Heat lost = heat gained
1 x 4.2 x 10³ x ( 93.33 - t ) = .25 x .385 x 10³ x ( t + 12.072 )
93.33 - t = .0229 ( t + 12.072)
93.33 - t = .0229 t + .276
93.054 = 1.0229 t
t = 90.97⁰C .
Answer:
Moreover, Boss says that even if Jupiter is proven to have a core, the planet still could have formed that core through disk instability. Enough dust could have collected and cemented together in the dense gas to form a core many times larger than the size of the Earth.
Explanation:
The same is true of most other objects in the solar system — except Jupiter. The gas giant is so big that it pulls the center of mass between it and the sun, also known as the barycenter, some 1.07 solar radii from the star's center — which is about 30,000 miles above the sun's surface.
69,911 km
69,911 kmJupiter/Radius
The emf will be induced in anti-clockwise direction.
<u>Explanation</u>
Lenz's law tells us the direction us the direction that the current will flow. It states that the direction is always such that it will oppose the change in flux which produced it. This means that any magnetic field produced by an induced current will be in opposite direction to the change in the original field.
To find the direction of emf, Stretch the forefinger, middle finger and the thumb of the right hand mutually perpendicular to each other. If the force finger points in the direction of the magnetic field, the thumb gives the direction of the motion of the conductor then the middle finger gives the direction of the induced current.
