You just landed on the planet Olympus IV, famous for its sports competitions. It's a light planet: the average density is one quarter of the Earths average density. It's also a large planet: the diameter is the double of the Earths diameter. The Olympians are giving a high jump competition, and one crew member takes part. You know that on Earth he jumps 1.98 meters. The record at Olympus IV is 3.86 meters. Should you bet your salary on him winning the competition ?

(In reply to

Answer by K Sengupta)

Let us denote:

D_L = average density of Olympus IV

D_E = average density of Earth

G_L = gravitation of Olympus IV

G_E = gravitation of Earth

m_L = mass of Olympus IV

m_E = mass of Earth

R_L = radius of Olympus IV

R_E = radius of Earth

V_L = volume of Olympus IV

V_E = volume of Earth

M = mass of the athlete

It is given that:

(i) R_L = 2*R_E, and (ii) D_L = 0,25*D_E

Now, we know that:

Average density varies directly(vd) as the volume.

Thus, V_L vd R_L^3, and:

V_L vd r_E^3, so that from (ii), we obtain:

V_L/V_E = 8

Now, m = D*V

-> m_L/m_E = 8*o,25 = 2

-> m_L = 2*m_E

Then,

G_L/G_E

= (m_L*M)/(R_l^2)*(m_E*m/R_E^2)^-1

= 2/4

= 0.5

Let the respective height to which the crew member can jump on Olympus

IV and Earth be h_L and h_E.

Let c be the gravitational center.

Then,

g_L/g_E = (h_L - c)/(h_E - c)

Now, we know that c = 1 meter and it is given that: h_E = 1.98 meters

Thus,

h_L = 2(1.98 - 1)

-> h_L = 2.96 meters.

Consequently, it would be unwise to bet one's salary upon the crew member winning the competition.

*Edited on ***December 15, 2008, 6:41 am**