Answer:
![t=14.678\times 10^{-3}s](https://tex.z-dn.net/?f=t%3D14.678%5Ctimes%2010%5E%7B-3%7Ds)
Explanation:
Given:
Capacitance, C = 85 pF = 85 × 10⁻¹² F
Resistance, R = 75 MΩ = 75×10⁶Ω
Charge in capacitor at any time 't' is given as:
![Q=Q_o(1-e^{-\frac{t}{RC}})](https://tex.z-dn.net/?f=Q%3DQ_o%281-e%5E%7B-%5Cfrac%7Bt%7D%7BRC%7D%7D%29)
where,
Q₀ = Maximum charge = CE
E = Initial voltage
t = time
also, Q = CV
V= Final voltage = 90% of E = 0.9E
thus, we have
![C\times 0.9E=CE(1-e^{-\frac{t}{75\times 10^6\ \times\ 85\times 10^{-12}}})](https://tex.z-dn.net/?f=C%5Ctimes%200.9E%3DCE%281-e%5E%7B-%5Cfrac%7Bt%7D%7B75%5Ctimes%2010%5E6%5C%20%5Ctimes%5C%2085%5Ctimes%2010%5E%7B-12%7D%7D%7D%29)
or
![0.9=1-e^{-\frac{t}{75\times 10^6\ \times\ 85\times 10^{-12}}}](https://tex.z-dn.net/?f=0.9%3D1-e%5E%7B-%5Cfrac%7Bt%7D%7B75%5Ctimes%2010%5E6%5C%20%5Ctimes%5C%2085%5Ctimes%2010%5E%7B-12%7D%7D%7D)
or
![e^{-\frac{t}{75\times 10^6\ \times\ 85\times 10^{-12}}}=1-0.9=0.1](https://tex.z-dn.net/?f=e%5E%7B-%5Cfrac%7Bt%7D%7B75%5Ctimes%2010%5E6%5C%20%5Ctimes%5C%2085%5Ctimes%2010%5E%7B-12%7D%7D%7D%3D1-0.9%3D0.1)
taking log both sides, we get
![ln(e^{-\frac{t}{75\times 10^6\ \times\ 85\times 10^{-12}}})=ln(0.1)=ln(\frac{1}{10})](https://tex.z-dn.net/?f=ln%28e%5E%7B-%5Cfrac%7Bt%7D%7B75%5Ctimes%2010%5E6%5C%20%5Ctimes%5C%2085%5Ctimes%2010%5E%7B-12%7D%7D%7D%29%3Dln%280.1%29%3Dln%28%5Cfrac%7B1%7D%7B10%7D%29)
or
![-\frac{t}{75\times 10^6\ \times\ 85\times 10^{-12}}=-ln(10)](https://tex.z-dn.net/?f=-%5Cfrac%7Bt%7D%7B75%5Ctimes%2010%5E6%5C%20%5Ctimes%5C%2085%5Ctimes%2010%5E%7B-12%7D%7D%3D-ln%2810%29)
or
![t=75\times 10^6\ \times\ 85\times 10^{-12}\times ln{10}](https://tex.z-dn.net/?f=t%3D75%5Ctimes%2010%5E6%5C%20%5Ctimes%5C%2085%5Ctimes%2010%5E%7B-12%7D%5Ctimes%20ln%7B10%7D)
or
![t=14.678\times 10^{-3}s](https://tex.z-dn.net/?f=t%3D14.678%5Ctimes%2010%5E%7B-3%7Ds)
1. Tectonic plates move
2. Magma forms and rises through the cracks
3. Lava flows onto the Earth’s surface
4. Lava cools and hardens to form igneous rock
In Nuclear Fusion, the reaction is involved in the merging of small atoms and high energy is produced, while in Nuclear Fission, it involves in the splitting of large atoms wherein radoactive isotopes are involved.
#1
When rocket is launched from the moon then there will be two forces on the rocket
1. Due to ejected gases the reaction force on rocket in forward direction
2. due to gravitational attraction of moon
So here we need to draw two arrow on its FBD in which first arrow is in the direction of motion of rocket which will be the reaction force on it while other arrow is opposite to its motion which is due to gravitational attraction force.
So answer would be TWO
#2
When crate is placed on the floor then in order to lift the crate upwards we always need an external force that will counter balance the normal force of crate.
Which mean if we make the normal force to be zero then crate will lift upwards and in order to make it zero we need to apply same force as that of normal force
So here the normal force is given as 150 N so we also need to apply 150 N force in order to lift it upwards
#3
If a person lift a box upwards by some force then we can say by force balance
Force applied by person + Normal force = Weight of the box
![F_{app} + F_n = mg](https://tex.z-dn.net/?f=F_%7Bapp%7D%20%2B%20F_n%20%3D%20mg)
we will plug in all values in it
![F_{app} + 150 = 30 * 10](https://tex.z-dn.net/?f=F_%7Bapp%7D%20%2B%20150%20%3D%2030%20%2A%2010)
![F_{app} = 300 - 150](https://tex.z-dn.net/?f=F_%7Bapp%7D%20%3D%20300%20-%20150)
![F_{app} = 150 N](https://tex.z-dn.net/?f=F_%7Bapp%7D%20%3D%20150%20N)
So we applied 150 N force on it
#4
In all cases we need to use force balance
like in case 3
![T + T = W](https://tex.z-dn.net/?f=T%20%2B%20T%20%3D%20W)
![2T = W](https://tex.z-dn.net/?f=2T%20%3D%20W)
![T = \frac{W}{2}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7BW%7D%7B2%7D)
so here in 3rd case tension is half of the weight
which will be the least tension in all cases
so answer is CASE 3