GATE-2018 (24) :Wyllie – Time average equation

GATE-2012

35. The distance between the center of the Earth and the barycentre (i.e center of mass of the Earth-Moon system) is (in Km)

A) 4510                B) 4670                 C) 4810            D) 4860

Solution:

Barycenter equation (x) =( m₂ /( m₁+m₂)) r_L ---------------(1)

r_L- is the distance from Earth- Moon (3,84,405 km)

m₂- mass of the moon ( 7.3477*10²² kg)

m₁ – mass of the Earth (5.97* 10²⁴ kg)

substitute above values in eq(1)

x= ( (7.3477* 10²²) / ( 7.3477*10²²+ 5.97*10²⁴) )* 3,84,405

x= ( (7.3477* 10²²) / ( 604.7477*10²²) )* 3,84,405

x= 0.01215 * 3,84,405

x= 4670.53 km

Therefore Barycenter (x) = 4670.53 km