Question

If the radius of the earth was half of its present
value and its mass (1/8)th of the present mass,
the value of g would have been reduced to
a) 1/8g
b) 1/2 g
c) 1/8
d) 8​

Answer 1

Answer:

Given:

Radius of Earth is made half.

Mass of Earth is made ⅛ of present mass.

To find:

New value of gravitational acceleration .

Formulas used:

$g = \frac{Gm}{ {r}^{2} }$

Calculation:

Let new gravity be g" , new radius be r" and new mass be m".

∴ g" = Gm"/(r")²

=> g" = {G (⅛m)}/(½r)²

=> g" = (4/8) [Gm/r²]

=> g" = ½ g .........[ as g = Gm/r²]

So the new gravity will become half of the present value ;

g" = ½g

Answer 2

$\huge{\orange{\underline{\red{\mathscr{GIVEN:-}}}}}$

If the radius of the earth was half of its present

value and its mass (1/8)th of the present mass.

$\huge{\orange{\underline{\red{\mathscr{FIND:-}}}}}$

gravitational acceleration

$\huge{\orange{\underline{\red{\mathscr{NOTE:-}}}}}$

GRAVITY IS DENOTE =G.

RADIUS IS DENOTE =R.

MASS IS DENOTE=M.

$\huge{\orange{\underline{\red{\mathscr{ANSWER:-}}}}}$

g'=GM'/(r')²

g'={g (1/8m)}/(½r) ²

g'=(4/8)[Gm /r²]

g'=½g ..... (according gravity formula g=gm/r²)

HENCE,

G'= ½g.

.°. gravitational acceleration is ½g.

$\huge{\orange{\underline{\red{\mathscr{THANKS.}}}}}$