Answer:
The time constant is 1.049.
Explanation:
Given that,
Charge 
We need to calculate the time constant
Using expression for charging in a RC circuit
![q(t)=q_{0}[1-e^{-(\dfrac{t}{RC})}]](https://tex.z-dn.net/?f=q%28t%29%3Dq_%7B0%7D%5B1-e%5E%7B-%28%5Cdfrac%7Bt%7D%7BRC%7D%29%7D%5D)
Where,
= time constant
Put the value into the formula
![0.65q_{0}=q_{0}[1-e^{-(\dfrac{t}{RC})}]](https://tex.z-dn.net/?f=0.65q_%7B0%7D%3Dq_%7B0%7D%5B1-e%5E%7B-%28%5Cdfrac%7Bt%7D%7BRC%7D%29%7D%5D)





Hence, The time constant is 1.049.
Answer:
R = 98304.75 m = 98.3 km
Explanation:
The density of an object is given as the ratio between the mass of that object and the volume occupied by that object.
Density = Mass/Volume
Now, it is given that the density of Earth has become:
Density = 1 x 10⁹ kg/m³
Mass = Mass of Earth (Constant) = 5.97 x 10²⁴ kg
Volume = 4/3πR³ (Volume of Sphere)
R = Radius of Earth = ?
Therefore,
1 x 10⁹ kg/m³ = (5.97 x 10²⁴ kg)/[4/3πR³]
4/3πR³ = (5.97 x 10²⁴ kg)/(1 x 10⁹ kg/m³)
R³ = (3/4)(5.97 x 10¹⁵ m³)/π
R = ∛[0.95 x 10¹⁵ m³]
<u>R = 98304.75 m = 98.3 km</u>
Answer:
a= 92. 13 m/s²
Explanation:
Given that
Amplitude ,A= 0.165 m
The maximum speed ,V(max) = 3.9 m/s
We know that maximum velocity in the SHM given as
V(max) = ω A
ω=Angular speed
A=Amplitude

ω=23.63 rad/s
The maximum acceleration given as
a = ω² A
a= (23.63)² x 0.165 m/s²
a= 92. 13 m/s²
Therefore the maximum magnitude of the acceleration will be 92. 13 m/s².