If the density of the earth is doubled keeping radius constant, find the new acceleration due to gravity? (g = 9.8 m/s2)

Question

If the density of the earth is doubled keeping radius constant, find the new acceleration due to gravity? (g = 9.8 m/s2)  (A)  9.8 m/s2  (B)  19.6 m/s2  (C)  4.9 m/s2  (D)  39.2 m/s2

Tardigrade Admin · Accepted Answer

Acceleration due to gravity g=(4/3) π ρ G R or g propto d R [∵. density .d=(4/3) π ρ] ∴ (g1/g2)=(d1/d2) (g1/g2)=(d/2 d) (∵ d2=2 d) g2=g1 × 2=9.8 × 2 g2=19.6 m / s 2

Q. If the density of the earth is doubled keeping radius constant, find the new acceleration due to gravity? $(g = 9.8 m / s^{2})$

$9.8 m / s^{2}$

$19.6 m / s^{2}$

$4.9 m / s^{2}$

$39.2 m / s^{2}$

Acceleration due to gravity $g = \frac{4}{3} π ρGR$
or $g \propto d R$ $[∵$ density $d = \frac{4}{3} π ρ]$
$∴ \frac{g _{1}}{g _{2}} = \frac{d _{1}}{d _{2}}$
$\frac{g _{1}}{g _{2}} = \frac{d}{2 d} (∵ d_{2} = 2 d)$
$g_{2} = g_{1} \times 2 = 9.8 \times 2$
$g_{2} = 19.6 m / s^{2}$

Q. If the density of the earth is doubled keeping radius constant, find the new acceleration due to gravity? (g=9.8m/s2)

9.8m/s2

19.6m/s2

4.9m/s2

39.2m/s2