Explanation:
Data provided:
Area A = 10 cm×2 cm = 20×10⁻⁴ m²
Separation distance d between the plates = 1 mm = 1×10⁻³ m
Battery voltage, or emf = 100 V
Resistance = 1025 ohm
Solution:
In an RC circuit, the voltage across the plates varies with time t. At the outset, the voltage matches that of the battery, V₀ = emf = 100V. However, after a certain time t, both the resistance and capacitance alter this, leading to a final voltage V expressed as
Applying the natural logarithm to both sides,
(1)
Next, we can determine the capacitance using the plates' area.
C = ε₀A/d
= 
= 18×10⁻¹²F
We can now find the time it takes for the voltage to drop from 100 to 55 V by substituting C, V₀, V, and R values into equation (1)
= -(1025Ω)(18×10⁻¹² F) ln( 1 - 55/100)
= 15×10⁻⁹s
= 15 ns
mass₃<mass₁=mass₅<mass₂=mass₄
Explanation:
Data points:-
1. mass: m speed: v
2. mass: 4 m speed: v
3. mass: 2 m speed: ¼ v
4. mass: 4 m speed: v
5. mass: 4 m speed: ½ v
We know that the formula for Kinetic energy (KE) is ½ mv²
Where m represents the mass of the object
v represents the object's velocity
<psubstituting the="" given="" values="" for="" mass="" and="" speed="" from="" previous="" data:="">
The KE of Body 1(mass₁) = ½*m*v² = mv²/2
KE of Body 2(mass₂) = ½*4m*v² = 2mv²
KE of Body 3(mass₃) = ½*2m*(1/4v)² = mv²/16
KE of Body 4(mass₄) = ½*4m*v ² = 2mv
²
KE of Body 5(mass₅) = ½*4m*(1/2v)² = mv²/2
</psubstituting>
Answer:
Induced EMF is 2 x 10⁻³ volts
Explanation:
B = strength of the magnetic field aligning with the loop's axis = 1 T
= area change rate of the loop = 20 cm²/s = 20 x 10⁻⁴ m²
θ = the angle formed by the magnetic field and area vector = 0
E = the induced EMF across the loop
EMF can be calculated using the formula
E = B
E = (1) (20 x 10⁻⁴ )
E = 2 x 10⁻³ volts
E = 2 mV
A basketball player maintains a steady pace of 2.5 m/s while throwing a basketball vertically at 6.0 m/s. How far does the player advance before getting the ball back? Air resistance is negligible. I was unsure which formula to apply to this scenario. Is there any relevance to an angle? First, we determine the duration to reach peak height. The total time for the flight will be double the ascent duration. According to Newton's equations of motion: v = u + at. At the highest point, v = 0, where u is 6 m/s. Thus, the equation becomes 0 = 6 - 9.81t, leading us to t = 0.61 seconds. Therefore, the total flight time equals 1.22 seconds as the player runs towards the ball at a horizontal speed of 2.5 m/s. The distance traveled can be calculated using distance = speed × time, resulting in distance = 2.5 m/s * 1.22, yielding a final distance of 6.11m.
The string does not experience any force of tension, as it balances two forces acting in the same direction. Hence, the tension is zero.
Explanation:
If tension existed in the string, it would mean that two equal but opposite forces are exerting pull in contrary directions.
When a force of f newtons is applied from the right and another force of f newtons from the left, the resulting action occurs through one force. Because there is action on the same string in opposing directions, the tension in the string can only be equal to the magnitude of the string itself.
Therefore, the string indeed has no tension since it is dealing with two forces acting in the same direction. Thus, the tension is zero.
