Answer
Verified
402.6k+ views
Hint: Write the equation for the gravitational force acting on a body on the surface of the Earth. From this equation derive the formula for acceleration due gravity. Now replace the value of radius with the new radius value and find out the new value for acceleration due to gravity. Compare both the values.
Complete step by step solution:
The gravitational forces acting on a body on the surface of the Earth is given by
$F=\dfrac{GMm}{{{R}^{2}}}$
Where,
G is universal constant of gravitation
M is the mass of the Earth
m is the mass of the body
Equating this Equation with $F=ma$, where a is the acceleration of a body, we get
$\begin{align}
& ma=\dfrac{GMm}{{{R}^{2}}} \\
& \therefore a=\dfrac{GM}{{{R}^{2}}} \\
\end{align}$
This is the acceleration with a body falling towards the center of the Earth.
We call this acceleration as acceleration due to gravity and denote it by ‘g’.
Thus,
$g=\dfrac{GM}{{{R}^{2}}}$
Now, this is the value of acceleration of a body at the surface of the Earth.
Given that, radius of earth is increased by 1% and its mass mass remains same, then the new radius is
\[\begin{align}
& {R}'=\text{ }R+\dfrac{1}{100}R \\
& {R}'=1.01R \\
\end{align}\]
The value acceleration due to gravity becomes
$g'=\dfrac{GM}{{{(R')}^{2}}}$
$\begin{align}
& {g}'=\dfrac{GM}{{{(1.01R)}^{2}}} \\
& \therefore {g}'=0.98g \\
\end{align}$
Since, ${g}' < g$, the value of acceleration due to gravity decreases.
$\begin{align}
& \%\text{ decrease in g = }\dfrac{g-{g}'}{g}\times 100 \\
& \%\text{ decrease in g}=\dfrac{g-0.98g}{g}\times 100 \\
& \%\text{ decrease in g}=2 \\
\end{align}$
Thus, the acceleration due to gravity on the surface of the Earth will decrease by 2%
Answer- B. Decrease by 2%
Note: Acceleration due to gravity is the acceleration of the body with which it falls towards the center of the Earth due to the gravitational force of attraction. It depends on the mass of the Earth and the distance of the body from the center of the Earth.
Complete step by step solution:
The gravitational forces acting on a body on the surface of the Earth is given by
$F=\dfrac{GMm}{{{R}^{2}}}$
Where,
G is universal constant of gravitation
M is the mass of the Earth
m is the mass of the body
Equating this Equation with $F=ma$, where a is the acceleration of a body, we get
$\begin{align}
& ma=\dfrac{GMm}{{{R}^{2}}} \\
& \therefore a=\dfrac{GM}{{{R}^{2}}} \\
\end{align}$
This is the acceleration with a body falling towards the center of the Earth.
We call this acceleration as acceleration due to gravity and denote it by ‘g’.
Thus,
$g=\dfrac{GM}{{{R}^{2}}}$
Now, this is the value of acceleration of a body at the surface of the Earth.
Given that, radius of earth is increased by 1% and its mass mass remains same, then the new radius is
\[\begin{align}
& {R}'=\text{ }R+\dfrac{1}{100}R \\
& {R}'=1.01R \\
\end{align}\]
The value acceleration due to gravity becomes
$g'=\dfrac{GM}{{{(R')}^{2}}}$
$\begin{align}
& {g}'=\dfrac{GM}{{{(1.01R)}^{2}}} \\
& \therefore {g}'=0.98g \\
\end{align}$
Since, ${g}' < g$, the value of acceleration due to gravity decreases.
$\begin{align}
& \%\text{ decrease in g = }\dfrac{g-{g}'}{g}\times 100 \\
& \%\text{ decrease in g}=\dfrac{g-0.98g}{g}\times 100 \\
& \%\text{ decrease in g}=2 \\
\end{align}$
Thus, the acceleration due to gravity on the surface of the Earth will decrease by 2%
Answer- B. Decrease by 2%
Note: Acceleration due to gravity is the acceleration of the body with which it falls towards the center of the Earth due to the gravitational force of attraction. It depends on the mass of the Earth and the distance of the body from the center of the Earth.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
Write an application to the principal requesting five class 10 english CBSE
What is the type of food and mode of feeding of the class 11 biology CBSE
Name 10 Living and Non living things class 9 biology CBSE