Answer

Verified

386.4k+ views

**Hint:**Express the new mass and radius of the earth as per given in the question. Recall the expression for the acceleration due to gravity and express the new acceleration due to gravity of the earth with new mass and radius. Calculate the decrease in the acceleration due to gravity.

**Formula used:**

Acceleration due to gravity, \[g = \dfrac{{GM}}{{{R^2}}}\]

Here, G is the gravitational constant, M is the mass of the earth and R is the radius of the earth.

**Complete step by step answer:**

We know the expression for the acceleration due to gravity of the planet,

\[g = \dfrac{{GM}}{{{R^2}}}\] ……. (1)

Here, G is the gravitational constant, M is the mass of the earth and R is the radius of the earth.

We have given that the mass of the earth has decreased by 25%. Therefore, the new mass of the earth is,

\[M' = M - 25\% M = M - \dfrac{M}{4}\]

\[ \Rightarrow M' = \dfrac{3}{4}M\] …… (2)

Also, the radius of the earth increases by 50%. Therefore, the new radius of the earth is,

\[R' = R + 50\% R = R + \dfrac{R}{2}\]

\[ \Rightarrow R' = \dfrac{3}{2}R\] …… (3)

Now, let us express the new acceleration due to gravity of the earth with new mass and radius as follows,

\[g' = \dfrac{{GM'}}{{{{R'}^2}}}\]

Using equation (2) and (3) in the above equation, we get,

\[g' = \dfrac{{G\left( {\dfrac{3}{4}M} \right)}}{{{{\left( {\dfrac{3}{2}R} \right)}^2}}}\]

\[ \Rightarrow g' = \dfrac{1}{3}\dfrac{{GM}}{{{R^2}}}\]

Using equation (1) in the above equation, we get,

\[g' = \dfrac{g}{3}\]

\[ \Rightarrow g' = 0.33\,g\]

Now, the net decrease in the acceleration due to gravity of the earth is,

\[\Delta g = g - g'\]

\[ \Rightarrow \Delta g = g - 0.33g\]

\[ \therefore \Delta g = 67\% \]

Therefore, the acceleration of the gravity of the earth decreases by 67%.

**So, the correct answer is option C.**

**Note:**While determining the decrease in the acceleration due to gravity, students must subtract the new acceleration due to gravity from the initial acceleration due to gravity. Note that the acceleration due to gravity is inversely proportional to the square of the radius of the planet and not just the radius. The universal gravitational constant remains constant even if there is change in the radius and change in mass of the planet or any other heavenly object.

Recently Updated Pages

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Name 10 Living and Non living things class 9 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

Write the 6 fundamental rights of India and explain in detail