Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

182 Aptitude Test Problems in Physics

the velocity v of the station immediately after

the collision through the relation

VR

2 =v2x/i•

(4)

Solving Eqs. (1)-(4) together and considering that

vf = ii-GM/R, we determine the velocity of the

meteorite before the collision:

. 17 58GM
u=
R •

1.83. For a body of mass m resting on the equator

of a planet of radius R, which rotates at an angu-

lar velocity w, the equation of motion has the

form

mco 2 R = mg' — N,

where N is the normal reaction of the planet sur-

face, and g' = 0.0Ig is the free-fall acceleration on

the planet. By hypothesis, the bodies on the equa-

tor are weightless, i.e. N = 0. Considering that

w = 2n/T, where T is the period of rotation of

the planet about its axis (equal to the solar day),

we obtain

,

R= 111 3 g -

Substituting the values T = 8.6 X 10' a and
g' 0.1 m/s 3 , we get

1.8 X 10 7 m = 18 000 km.

1.84. We shall write the equation of motion for

Neptune and the Earth around the Sun (for the

sake of simplicity, we assume that the orbits are

circular):

GMmN

mNwNRN = R2

G

MARE

MME

RI •