Question

Captain Kirk has crash landed on an unknown planet (planet X). With nothing to do while waiting for rescue , he decides to think about physics and to learn about the planet he's on. He takes out a simple pendulum (a mass on a string), and notices that for small oscillations , the period is T = 2.0 seconds . Back on Earth', this same pendulum had a period of 1.5 seconds . Kirks' ship computer says that the radius of planet X is 3 times larger than Earth's radius. Determine the mass of planet X.

Answer 1

Step 1: FInd acceleration due to gravity on the unknown planet:

We know that time period of a simple pendulum is given by:

T = 2*pi*sqrt (L/g)

Since length of pendulum remains constant, So

T2/T1 = sqrt (g1/g2)

T2 = Time period on the earth = 1.5 sec

T1 = Time period on the unknown planet = 2.0 sec

g2 = gravity due to acceleration on earth = 9.81 m/s^2

So, g1 = gravity due to acceleration on unknown planet = ?

g1 = g2*(T2/T1)^2

g1 = 9.81*(1.5/2.0)^2 = 5.52 m/s^2

Step 2: Find Mass of planet X using gravitational acceleration

We know that:

g = acceleration of due to gravity on planet X = G*M/R^2 = 5.52 m/s^2

M = mass of planet X = ?

G = Gravitational constant = 6.67*10^-11

R = Radius of planet X = 3*Radius of planet Earth

R = 3*6.37*10^6 m

So,

M = g*R^2/G

Using known values:

M = 5.52*(3*6.37*10^6)^2/(6.67*10^-11)

M = 3.02*10^25 kg = Mass of planet X

Let me know if you've any query.

answered by: anonymous