Question

If both the mass and the radius decrease by $1\%$ then the decrease in g will be nearly,

• A. $1\%$
• B. $3\%$
• C. $6\%$
• D. $10\%$

Answer 1

The correct option is A

$1\%$

Explanation for correct option:

Step 1: Given

Original mass$=M$

Original radius$=R$

New mass $=M-1\%\left(M\right)$

$$\begin{gathered} =M-0.01M \\ =0.99M \end{gathered}$$

New radius$=R-1\%\left(R\right)$

$$\begin{gathered} =R-0.01R \\ =0.99R \end{gathered}$$

Step 2: Formula used

Acceleration due to gravity is given by $g=\frac{GM}{R^2}$

Where g is the acceleration due to gravity, G is the gravitational constant, M is the mass and R is the radius.

Step 3: Determine the value of g

If both the mass and the radius decrease by $1\%$ then g is given by,

$$\begin{gathered} g\text{'}=\frac{G(0.99M)}{{(0.99R)}^2} \\ =1.01\frac{GM}{R^2} \\ =1.01g \end{gathered}$$

Hence, option (A) is the correct option.