Question

Choose the correct alternativea. If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/potential energy.b. The energy required to launch an orbiting satellite out of earth's gravitational influence is more/less than the energy required to project a stationary object at the same height (as the satellite) out of earth's influence.

Answer 1

We know,

Potential energy of satellite(P.E) = -GMm/r

Kinetic energy of satellite(K.E) = GMm/2r

Total energy = P.E + K.E

= -GMm/r + GMm/2r

= -GMm/2r = -K.E

e.g the total energy of an orbiting satellite is negative of the kinetic energy.

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(B) the energy required to rocket an orbiting satellite out of earth' s Gravitational influence is less than the energy required to ptpject a stationary object , becoz , in case of orbiting satellite the Gravitational pull of earth acting on it is balance by centripetal force so, no work is required against the Gravitational pull.

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Answer 2

Answer:

Let initial force of attraction between two objects is F when distance between objects is r.

But force of attraction decreased by 36% when the distance between them is increased by 4.

e.g., final force = F - 36% F = 0.64F

We know, gravitational force is inversely proportional to square of distance between objects.

so, \frac{F_1}{F_2}=\frac{d_2^2}{d_1^2}

F

2

F

1

=

d

1

2

d

2

2

or, \frac{F}{0.64F}=\frac{(r+4)^2}{r^2}

0.64F

F

=

r

2

(r+4)

2

or, 1/(0.8)² = (r + 4)/r

or, 1/ 0.8 = (r + 4)/r

or, r = 0.8r + 3.2

or, r = 16 m

hence, original distance between them is 16m