Question

A body is projected up with a velocity equal to $\frac { 3 } { 4 }$th of the escape velocity from the surface of the earth. The height it reaches from the centre of the earth is : (Radius of the earth = R) :

• A.
• B. $\frac { 16 R } { 7 }$
• C. $\frac { 9 \mathrm { R } } { 8 }$
• D.

Answer 1

Answer: (B)

$\frac { 16 R } { 7 }$

Answer 2

v = $\frac { 3 } { 4 }$ v_e

K.E. = $\frac { 1 } { 2 }$ mv² = $\frac { 1 } { 2 }$m

= $\frac { 9 } { 32 }$

= $\frac { 9 } { 32 }$ m

K.E = $\frac { 9 } { 16 }$

P.E. =

Total energy = K.E. +

P.E. = $- \frac { 7 } { 16 }$

Let the height above the surface of earth be h; then P.E. = $- \frac { \mathrm { GMm } } { \mathrm { h } }$

Total energy = P.E. above earth's surface

$- \frac { 7 } { 16 }$ $\frac { \mathrm { GMm } } { \mathrm { R } }$ = –

$\therefore$h =