Question

A body is projected up with a velocity equal to (3/4)th of the escape velocity from the surface of the earth. The height it reaches is- (Radius of earth = R)

• A.
• B.
• C.
• D. $\frac { 10 \mathrm { R } } { 3 }$

Answer 1

Answer: (B)

Answer 2

Escape velocity for the earth is

v_e =

Given the velocity projection of the body

= v = $\frac { 3 } { 4 }$ $\sqrt { \frac { 2 \mathrm { GM } } { \mathrm { R } } }$

Total energy on the earth = Total enery at maximum height h

$\frac { 1 } { 2 }$mv² += 0 +

$\frac { 1 } { 2 }$m . $\frac { 9 } { 16 }$ . $\frac { 2 \mathrm { GM } } { \mathrm { R } }$ – = $- \frac { \mathrm { GMm } } { \mathrm { R } + \mathrm { h } }$

$\frac { 9 } { 16 } - 1$ = – or – $\frac { \mathrm { R } } { \mathrm { R } + \mathrm { h } }$ = $\frac { - 7 } { 16 }$

7R + 7h = 16 R

7h = 9R Ž h = $\frac { 9 } { 7 }$R