Gravitational force
F = GMm/R²
Gravitational intensity of earth at point A
I = F/m = GMm/R²/m
I = GM/R²

We know that acceleration due to gravity from the surface of Earth at height "h" is given as,

{tex}g' = g \left( \frac { R } { R + h } \right) ^ { 2 }{/tex}
 reduced to 4% of gravity due to earth g' = 4% of {tex}g' = \frac { 4 g } { 100 }{/tex}
R = 6400km
{tex}\frac { 4 g } { 100 }= g \left( \frac { R } { R + h } \right) ^ { 2 }{/tex}
{tex}\frac { 4 } { 100 } = \left( \frac { R } { R + h } \right) ^ { 2 }{/tex}
{tex}\frac { 2 } { 10 } = \frac { R } { R + h }{/tex}
2(R + h) = 10R

2R+2h=10R
2h =10R-2R

2h=8R

h=8R/2
h = 4R

h= 4 {tex}\times{/tex} 6400

h= 25,600km.

Let us consider the two systems A and B and both the systems are isolated by adiabatic wall. That means neither energy nor matter can enter or leave either system. In this case both the systems cannot communicate through this wall since it is an adiabatic wall.
Now we replace the adiabatic wall with diathermic wall, which permits the flow of energy in the form of heat and finally it will reach thermal equilibrium.

Now instead of two systems, consider three systems A, B and C. The systems A and B are separated by an adiabatic wall, while each is in contact with a third system C, through a conducting wall.

The states of the systems which is characterized by certain macroscopic variables, will change until both A and B come into thermal equilibrium with C.

After this stage the adiabatic wall between the systems A and B is replaced by a conducting wall and the system C is insulated from A and B by an adiabatic wall.

Observation: We found that the states of A and B remains as in the previous case. That means both the systems are in thermal equilibrium with each other.

Observation Leads to Defining Law: "If two systems are at the same time in thermal equilibrium with a third system, they are in thermal equilibrium with each other. If A and C are in thermal equilibrium with B, then A is in thermal equilibrium with B". This statement is called as Zeroth Law.

Practically this means that all three are at the same temperature, and it forms the basis for comparison of temperatures.

The Zeroth law is more fundamental than first and second law even though actually it was stated much later than both the First and Second Laws of thermodynamics. It is so named because it logically precedes the First and Second Laws of Thermodynamics.

<font face="Verdana"><font style="text-shadow: rgba(255, 255, 255, 0.3) 0px 1px 1px; user-select: initial !important; line-height: 1.5em; -webkit-font-smoothing: antialiased; font-family: roboto, sans-serif; color: rgb(51, 51, 51); font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial;">The Zeroth Law clearly suggests that when two systems A and B, are in thermal equilibrium then there must be a physical quantity that has the same value for both the systems.</font></font>

<font face="Verdana"><font style="text-shadow: rgba(255, 255, 255, 0.3) 0px 1px 1px; user-select: initial !important; line-height: 1.5em; -webkit-font-smoothing: antialiased; font-family: roboto, sans-serif; color: rgb(51, 51, 51); font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial;">This physical quantity is a new thermodynamic parameter whose value is equal for two systems in thermal equilibrium and is called as temperature (T). This is the only property which allows us to think of the possible make and use of thermometer.</font></font>

<font face="Verdana"><font style="text-shadow: rgba(255, 255, 255, 0.3) 0px 1px 1px; user-select: initial !important; line-height: 1.5em; -webkit-font-smoothing: antialiased; font-family: roboto, sans-serif; color: rgb(51, 51, 51); font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial;">If A and B are separately in equilibrium with C, then</font></font>
<font face="Verdana"><font style="text-shadow: rgba(255, 255, 255, 0.3) 0px 1px 1px; user-select: initial !important; line-height: 1.5em; -webkit-font-smoothing: antialiased; font-family: roboto, sans-serif; color: rgb(51, 51, 51); font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial;">T_A = T_C</font></font><font color="#ff0000"><font face="Verdana"><font style="text-shadow: rgba(255, 255, 255, 0.3) 0px 1px 1px; user-select: initial !important; line-height: 1.5em; -webkit-font-smoothing: antialiased; font-family: roboto, sans-serif; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial;"> </font></font></font><font face="Verdana"><font style="text-shadow: rgba(255, 255, 255, 0.3) 0px 1px 1px; user-select: initial !important; line-height: 1.5em; -webkit-font-smoothing: antialiased; font-family: roboto, sans-serif; color: rgb(51, 51, 51); font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial;">and T_B = T_C</font></font>
This leads to T_A = T_B

<font face="Verdana"><font style="text-shadow: rgba(255, 255, 255, 0.3) 0px 1px 1px; user-select: initial !important; line-height: 1.5em; -webkit-font-smoothing: antialiased; font-family: roboto, sans-serif; color: rgb(51, 51, 51); font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial;">i.e. the systems A and B are also in thermal equilibrium.</font></font>

We know that
v^2 = u^2 + 2aS
v= final velocity
u= initial velocity
a= acceleration due to gravity
S = displacement
S= (v^2 - u^2)÷2a
Work done= force * displacement
W = F * S
F= ma
W= ma * (v^2 - u^2)÷2a
W= 1/2 * m* (v^2-u^2)
If u=0 ( body starts from rest)
W= 1/2 * m * v^2=Kinetic energy

Let the force of smaller magnitude be A and the force of larger magnitude be B.

here,it is clearly given that the resultant force is R perpendicular to small force. hence, we can say that b is the hyopetenuse .

therefore, b² = R² + A²
=> R² = b² - A²
= 8²
= 64 .......................... ( 1 ).

here, it is also given that
A + B = 16
therefore , B = 16 - A ..........................( 2 ).

Now, by substituting ( 2 ) in ( 1 ).we get,

( 16 - A ) ²- A² = 64
=> 256 - 32A + A² - A² = 64
32A = 256 - 64 = 192
A = 192 / 32
= 6

hence, we get the result
B = 16 - A = 16 - 6 = 10

Therefore, the magnitude of the two vectors are 6 and 10.

1N = 100000 dynes = 10⁵ dynes
1m² = 10000 cm² = 10⁴ cm²
1N/m² = 10⁹ dynes/cm²
So 19 {tex}\times{/tex}10¹⁰ N/m² = 19 {tex}\times{/tex}10¹⁰{tex}\times{/tex}10⁹ = 1.9 {tex}\times{/tex}10²⁰ dynes/cm²