Question

A particle of mass m is projected upwards with velocity v = , where v_e is the escape velocity then at the maximum height the potential energy of the particle is : (R is radius of earth and M is mass of earth)

• A. $\frac { - \mathrm { GMm } } { 2 \mathrm { R } }$
• B. $\frac { - \mathrm { GMm } } { 4 \mathrm { R } }$
• C.
• D. $\frac { - 2 \mathrm { GMm } } { 3 \mathrm { R } }$

Answer 1

Answer: (C)

Answer 2

When only conservative forces are acting, mechanical energy is conserved and at maximum height speed is zero.

$\frac { - \mathrm { GMm } } { \mathrm { R } } + \frac { 1 } { 2 } \mathrm {~m} \left( \frac { \mathrm { v } _ { \mathrm { e } } } { 2 } \right) ^ { 2 }$= U + 0

$\frac { - \mathrm { GMm } } { \mathrm { R } } + \frac { 1 } { 2 } \mathrm {~m} \left( \frac { \mathrm { GM } } { 2 \mathrm { R } } \right) = \mathrm { U }$

U = =