So that the next generation could inherit the previous adaptations and instinct and be similar to the parents. if that didn't happen, a cat might give birth to a giraffe
Answer:
5.7 x 10^12 C
Explanation:
Let the charge on earth and moon is q.
mass of earth, Me = 5.972 x 10^24 kg
mass of moon, Mm = 7.35 x 10^22 kg
Let d be the distance between earth and moon.
the gravitational force between them is
![F_{g}=G\frac{M_{e} \times M_{m}}{d^{2}}](https://tex.z-dn.net/?f=F_%7Bg%7D%3DG%5Cfrac%7BM_%7Be%7D%20%5Ctimes%20M_%7Bm%7D%7D%7Bd%5E%7B2%7D%7D)
The electrostatic force between them is
![F_{e}=\frac{Kq^{2}}{d^{2}}](https://tex.z-dn.net/?f=F_%7Be%7D%3D%5Cfrac%7BKq%5E%7B2%7D%7D%7Bd%5E%7B2%7D%7D)
According to the question
1 % of Fg = Fe
![0.01 \times 6.67\times10^{-11}\frac{5.97 \times 10^{24}\times7.35 \times 10^{22}}{d^{2}}=9 \times 10^{9}\frac{q^{2}}{d^{2}}](https://tex.z-dn.net/?f=0.01%20%5Ctimes%206.67%5Ctimes10%5E%7B-11%7D%5Cfrac%7B5.97%20%5Ctimes%2010%5E%7B24%7D%5Ctimes7.35%20%5Ctimes%2010%5E%7B22%7D%7D%7Bd%5E%7B2%7D%7D%3D9%20%5Ctimes%2010%5E%7B9%7D%5Cfrac%7Bq%5E%7B2%7D%7D%7Bd%5E%7B2%7D%7D)
![2.927 \times 10^{35}=9 \times10^{9}q^{2}](https://tex.z-dn.net/?f=2.927%20%5Ctimes%2010%5E%7B35%7D%3D9%20%5Ctimes10%5E%7B9%7Dq%5E%7B2%7D)
![3.25 \times 10^{25}=q^{2}](https://tex.z-dn.net/?f=3.25%20%5Ctimes%2010%5E%7B25%7D%3Dq%5E%7B2%7D)
q = 5.7 x 10^12 C
Thus, the charge on earth and the moon is 5.7 x 10^12 C.
m = mass of the penny
r = distance of the penny from the center of the turntable or axis of rotation
w = angular speed of rotation of turntable
F = centripetal force experienced by the penny
centripetal force "F" experienced by the penny of "m" at distance "r" from axis of rotation is given as
F = m r w²
in the above equation , mass of penny "m" and angular speed "w" of the turntable is same at all places. hence the centripetal force directly depends on the radius .
hence greater the distance from center , greater will be the centripetal force to remain in place.
So at the edge of the turntable , the penny experiences largest centripetal force to remain in place.
Answer: 2.94×10^8 J
Explanation:
Using the relation
T^2 = (4π^2/GMe) r^3
Where v= velocity
r = radius
T = period
Me = mass of earth= 6×10^24
G = gravitational constant= 6.67×10^-11
4π^2/GMe = 4π^2 / [(6.67x10^-11 x6.0x10^24)]
= 0.9865 x 10^-13
Therefore,
T^2 = (0.9865 × 10^-13) × r^3
r^3 = 1/(0.9865 × 10^-13) ×T^2
r^3 = (1.014 x 10^13) × T^2
To find r1 and r2
T1 = 120min = 120*60 = 7200s
T2 = 180min = 180*60= 10800s
Therefore,
r1 = [(1.014 x 10^13)7200^2]^(1/3) = 8.07 x 10^6 m
r2 = [(1.014 x 10^13)10800^2]^(1/3) = 10.57 x 10^6 m
Required Mechanical energy
= - GMem/2 [1/r2 - 1/r1]
= (6.67 x 10^-11 x 6.0 x 10^24 * 50)/2 * [(1/8.07 × 10^-6 )- (1/10.57 × 10^-6)]
= (2001 x 10^7)/2 * (0.1239 - 0.0945)
= (1000.5 × 10^7) × 0.0294
= 29.4147 × 10^7 J
= 2.94 x 10^8 J.
Answer:9.34 A/s
Explanation:
Given
radius of solenoid ![R=1.06 m](https://tex.z-dn.net/?f=R%3D1.06%20m)
Emf induced ![E=8.50\times 10^{-6} V/m](https://tex.z-dn.net/?f=E%3D8.50%5Ctimes%2010%5E%7B-6%7D%20V%2Fm)
no of turns per meter n=450
we know Induced EMF is given by
![\int Edl=-\frac{\mathrm{d} \phi}{\mathrm{d} t}=-\frac{\mathrm{d} B}{\mathrm{d} t}A](https://tex.z-dn.net/?f=%5Cint%20Edl%3D-%5Cfrac%7B%5Cmathrm%7Bd%7D%20%5Cphi%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D-%5Cfrac%7B%5Cmathrm%7Bd%7D%20B%7D%7B%5Cmathrm%7Bd%7D%20t%7DA)
Magnetic Field is given by
![B=\mu _0ni](https://tex.z-dn.net/?f=B%3D%5Cmu%20_0ni)
thus ![\frac{\mathrm{d} B}{\mathrm{d} t}=-\mu _0n\frac{\mathrm{d} i}{\mathrm{d} t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20B%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D-%5Cmu%20_0n%5Cfrac%7B%5Cmathrm%7Bd%7D%20i%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
Area of cross-section
where
solving integration we get
![E.\cdot 2\pi r=\mu _0n\frac{\mathrm{d} i}{\mathrm{d} t}\pi R^2](https://tex.z-dn.net/?f=E.%5Ccdot%202%5Cpi%20r%3D%5Cmu%20_0n%5Cfrac%7B%5Cmathrm%7Bd%7D%20i%7D%7B%5Cmathrm%7Bd%7D%20t%7D%5Cpi%20R%5E2)
where r=distance from axis
R=radius of Solenoid
![\frac{\mathrm{d} i}{\mathrm{d} t}=\frac{Er}{\mu _0nR^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20i%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D%5Cfrac%7BEr%7D%7B%5Cmu%20_0nR%5E2%7D)
![\frac{\mathrm{d} i}{\mathrm{d} t}=\frac{8.50\times 10^{-6}\times 3.49\times 10^{-2}}{4\pi \times 10^{-7}\times 450\times 1.06^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20i%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D%5Cfrac%7B8.50%5Ctimes%2010%5E%7B-6%7D%5Ctimes%203.49%5Ctimes%2010%5E%7B-2%7D%7D%7B4%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%5Ctimes%20450%5Ctimes%201.06%5E2%7D)
![\frac{\mathrm{d} i}{\mathrm{d} t}=9.34 A/s](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20i%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D9.34%20A%2Fs)