Question

State Newton's second law of motion. Give its mathematical Equation.
(b) Difference between acceleration due to gravity (g) and Universal Gravitational constant (G).


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Answer 1

[ 1 ]

$\underline{ \huge \pink{ \bf2^{nd} \: Law \: of \: Motion.}}$

★ The rate of change of momentum with respect to time of an object is directly proportional to the applied balanced force in the direction of the force.

Mathematicaly Derivation :-

$\implies \sf \: \Delta p = Initial \: Momentum - Final \: Momentum$

$\implies \sf \: \Delta p =mv - mu$

$\implies \sf \: \Delta p =m(v -u) -------(1) \:$

Now According to Newton's second law of motion, The rate of change of momentum with respect to time of an object is directly proportional to the applied balanced force so,

$\implies \sf \: \dfrac{\Delta p}{t} \propto F$

$\implies \sf \: F \propto \dfrac{m(v - u)}{t} \: \: \: \: \: \: \: \: \: \: \: \bigg \lgroup \: \because \: from \: (1) \bigg \rgroup$

Now from the formula of Acceleration we have,

$\implies \sf \: F \propto ma$

Now put the praportionality constant,

$\implies \sf \: F = kma$

$\implies \sf \: F =ma \: \: \: \: \: \: \: \: \: \: \: \: \: \bigg \lgroup \: \because \: k = 1\bigg \rgroup$

Hence Derived !

[ 2 ]

★ Acceleration due to gravity ( g ) :- The Acceleration which is produced due to gravitational force who is called as Acceleration due to gravity ( g ). It's SI unit is m/s² and the value of g is 9.8 m/s² on earth.

★ Universal law of gravitation :- This law stats that Force of attraction between any two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them i.e ( F = G Mm/d² )

where G is the universal gravitational constant. It's SI unit is N m²/kg².

Answer 2

Given :-

State Newton's second law of motion. Give its mathematical Equation.

(b) Difference between acceleration due to gravity (g) and Universal Gravitational constant (G).

Answers :-

1]

Newton second law of motion says that acceleration of any object is directly related to the force force applied and indirectly related to its mass of the object.

The formula is f = ma

F is the force

m is the mass

a is the acceleration

Now,

2]

• Acceleration due to gravity is denoted as g. And Universal acceleration is denoted as G.
• Formula of acceleration due to gravity is F = mg where the formula for universal gravitation is$\sf F=(GM_{1}M_{2})/R^{2}$