A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity of 0.79 rad/s . Its total moment of inertia is 1790
1 answer:
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Answer:
The current in the circuit at a time interval of τ seconds after the switch has been closed is 0.123 A
Explanation:
The time constant for an R and C in series circuit is given by τ = RC.
R = 3000 ohms, C = 0.5 × 10⁻⁶ F = 5.0 × 10⁻⁷ F
τ = 3000 × 5 × 10⁻⁷ = 0.015 s
The voltage across a capacitor as it charges is given be
V(t) = Vs (1 - e⁻ᵏᵗ)
where k = 1/τ
At the point when t = τ, the expassion becomes
V(t = τ) = 1000 (1 - e⁻¹) = 0.632 × 1000 = 632 V
Current flows as a result of potential difference,.
Current in the circuit at this time t = τ is given by
I = (Vs - Vc)/R
Vs = source voltage = 1000 V
Vc = Voltage across the capacitor = 632 V
R = 3000 ohms
I = (1000 - 632)/3000 = 0.123 A
Answer:
5.3 x 10⁻⁹ C
Explanation:
r = radius of cylindrical shell = 10⁻⁵ m
L = length = 0.32 m
A = area
Area is given as
A = 2πrL
A = 2 (3.14) (10⁻⁵) (0.32)
A = 20.096 x 10⁻⁶ m²
d = separation = 10⁻⁸ m
= dielectric constant = 4
Capacitance is given as
eq-1
V = Potential difference across the membrane = 74 mV = 0.074 Volts
Q = magnitude of charge on each side
Magnitude of charge on each side is given as
Q = CV
using eq-1
Inserting the values
Q = 5.3 x 10⁻⁹ C
Given :
The acceleration due to gravity on or near the surface of Earth is 32 ft/s/s
To Find :
From what height must a stone be dropped on Earth to strike the ground with a velocity of 136 ft/s.
Solution :
Initial velocity of stone, u = 0 ft/s.
Now, by equation of motion :
Therefore, height from which stone is thrown is 289 ft.