Sophia asked in Science & MathematicsPhysics · 1 month ago

# Physics Question?

An object takes 2.55 s to fall 5.35 m on a certain planet. Find the planet's mass if its radius is 5250 km.

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• Anonymous
1 month ago

2h = g*t^2

g = 2h/t^2 = 10.7/2.55^2 = 1.646 m/sec^2 = M*G/r^2 (G = 6.674*10^-11)

M = g*r^2/G = 1.646*5.25^2*10^12*10^11/6.674 = 6.80*10^23 kg

• MyRank
Lv 6
1 month ago

Given,

Time (t) = 2.55 sec

Height (h) = 5.35 m

Mass (m) = ?

Radius (r) = 5250 km = 5250 x 10³m

We know that:-

Acceleration due to gravity (g) = Gm/r²

Mass (m) = gr²/G = 2hr²/t²G [∵ h = ½gt²]

2 x 5.35 x (5250 x 10³)² / (2.55)² x 6.67 x 10⁻¹¹

= 294918750 x 10⁶ / 43.37 x 10⁻¹¹≈ 6.80 x 10²³kg

∴ Mass (m) = 6.80 x 10²³kg.

• 1 month ago

d = distance of fall = 5.35 m

t = time of fall = 2.55 s

a = gravitational acceleration = to be determined

d = 0.5at²

2d = at²

2d/t² = a

a = 2d/t²

a = (2 x 5.35 m) / (2.55 s)²

a = 1.645520953 m/s² ≈ 1.65 m/s²

G = universal gravitational constant = 6.67E-11 N·m²/kg²

r = radius = 5,250 km = 5,250,000 m

m = mass = to be determined

m = ar²/G

m = (1.65 m/s²)(5.25E+06 m)²/(6.67E-11 N·m²/kg²)

• 1 month ago

h = ½gt²

5.35 = ½g(2.55)²

g = 2•5.35/(2.55)² = 1.646 m/s²

g = GM/r² = 1.646

M = (1.646)(5250000)² / 6.674e-11 = 6.80e23 kg or 6.80x10²³

• Dylan
Lv 6
1 month ago

s = 0.5*at^2 + vt

5.35 = 0.5*g*2.55^2

g = 1.6455 m/s^2

g = GM/r^2

M = gr^2/G

= 1.6455*5,250,000^2/(6.67408*10^-11)

= 6.80*10^23 kg