Question

Two identical satellites are at R and 7R away from earth surface, the wrong statement is (R = Radius of earth)

• A. Ratio of total energy will be 4
• B. Ratio of kinetic energies will be 4
• C. Ratio of potential energies will be 4
• D. Ratio of total energy will be 4 but ratio of potential and kinetic energies will be 2

Answer 1

Answer: (D)

Ratio of total energy will be 4 but ratio of potential and kinetic energies will be 2

Answer 2

Orbital radius of satellites $r _ { 1 } = R + R = 2 R$

$r _ { 2 } = R + 7 R = 8 R$

$U _ { 1 } = \frac { - G M m } { r _ { 1 } }$ and $U _ { 2 } = \frac { - G M m } { r _ { 2 } }$

$K _ { 1 } = \frac { G M m } { 2 r _ { 1 } }$ and $K _ { 2 } = \frac { G M m } { 2 r _ { 2 } }$

$E _ { 1 } = \frac { G M m } { 2 r _ { 1 } }$ and $E _ { 2 } = \frac { G M m } { 2 r _ { 2 } }$

∴$\frac { U _ { 1 } } { U _ { 2 } } = \frac { K _ { 1 } } { K _ { 2 } } = \frac { E _ { 1 } } { E _ { 2 } } = 4$