Answer:
The value is ![E = 1.35 *10^{14} \ J](https://tex.z-dn.net/?f=E%20%3D%20%201.35%20%2A10%5E%7B14%7D%20%5C%20J)
Explanation:
From the question we are told that
The mass of matter converted to energy on first test is ![m = 1 \ g = 0.001 \ kg](https://tex.z-dn.net/?f=m%20%20%3D%20%201%20%5C%20%20g%20%20%3D%200.001%20%5C%20%20kg)
The mass of matter converted to energy on second test ![m_1 = 1.5 \ g = 1.5 *10^{-3} \ kg](https://tex.z-dn.net/?f=m_1%20%3D%20%201.5%20%5C%20%20g%20%3D%201.5%20%2A10%5E%7B-3%7D%20%5C%20kg)
Generally the amount of energy that was released by the explosion is mathematically represented as
![E = m * c^2](https://tex.z-dn.net/?f=E%20%3D%20%20m%20%2A%20c%5E2)
=> ![E = 1.5 *10^{-3} * [ 3.0 *10^{8}]^2](https://tex.z-dn.net/?f=E%20%3D%20%201.5%20%2A10%5E%7B-3%7D%20%20%2A%20%5B%203.0%20%2A10%5E%7B8%7D%5D%5E2)
=> ![E = 1.35 *10^{14} \ J](https://tex.z-dn.net/?f=E%20%3D%20%201.35%20%2A10%5E%7B14%7D%20%5C%20J)
The electric field strength is inversely related to the square of the distance.so the strength of the electric field is given by
![E=\frac{1}{4\pi \epsilon _{0} } \frac{q}{r^{2} } = \frac{k q}{r^{2} }](https://tex.z-dn.net/?f=E%3D%5Cfrac%7B1%7D%7B4%5Cpi%20%5Cepsilon%20_%7B0%7D%20%20%7D%20%5Cfrac%7Bq%7D%7Br%5E%7B2%7D%20%7D%20%3D%20%5Cfrac%7Bk%20q%7D%7Br%5E%7B2%7D%20%7D)
Here,
is constant depend upon medium and its value is
and q is charge and r is the distance.
Given
and we know the charge of proton,
.
Therefore,
![E=\frac{9.0 \times10^{9} \ N m^2/C^2 \times1.6\times 10^{-19} \ C }{(9.0 \times 10^{-4} m)^2} = 0.177 \times 10^{-2} \ N/C \\\\ E= 1.77 \times 10^{-3} N/C](https://tex.z-dn.net/?f=E%3D%5Cfrac%7B9.0%20%5Ctimes10%5E%7B9%7D%20%5C%20N%20m%5E2%2FC%5E2%20%5Ctimes1.6%5Ctimes%2010%5E%7B-19%7D%20%5C%20C%20%20%7D%7B%289.0%20%5Ctimes%2010%5E%7B-4%7D%20m%29%5E2%7D%20%3D%200.177%20%5Ctimes%2010%5E%7B-2%7D%20%5C%20N%2FC%20%5C%5C%5C%5C%20%20E%3D%201.77%20%5Ctimes%2010%5E%7B-3%7D%20%20N%2FC)
Answer:
![g'_h=1.096\times 10^{-5}\ m.s^{-2}](https://tex.z-dn.net/?f=g%27_h%3D1.096%5Ctimes%2010%5E%7B-5%7D%5C%20m.s%5E%7B-2%7D)
Explanation:
We know that the gravity on the surface of the moon is,
<u>Gravity at a height h above the surface of the moon will be given as:</u>
..........................(1)
where:
G = universal gravitational constant
m = mass of the moon
r = radius of moon
We have:
is the distance between the surface of the earth and the moon.
Now put the respective values in eq. (1)
![g'_h=\frac{6.67\times 10^{-11}\times 7.35\times 10^{22}}{(1.74\times 10^6+384.4\times 10^6)^2}](https://tex.z-dn.net/?f=g%27_h%3D%5Cfrac%7B6.67%5Ctimes%2010%5E%7B-11%7D%5Ctimes%207.35%5Ctimes%2010%5E%7B22%7D%7D%7B%281.74%5Ctimes%2010%5E6%2B384.4%5Ctimes%2010%5E6%29%5E2%7D)
is the gravity on the moon the earth-surface.
Energy is measured by joule(j)