Question

A small block of superdense material has mass 2 × 10²⁴ kg. It is at a height h << R. It falls towards earth. Find its speed when it is at a height h/2 –

• A. $\sqrt { \frac { 2 \mathrm { gh } } { 3 } }$
• B. $\sqrt { \frac { 3 \mathrm { gh } } { 4 } }$
• C. $\sqrt { \frac { 3 \mathrm { gh } } { 5 } }$
• D.

Answer 1

Answer: (B)

$\sqrt { \frac { 3 \mathrm { gh } } { 4 } }$

Answer 2

m = 2 × 10²⁴ kg, M_earth = 6 × 10^–24 kg = $\frac { \mathrm { M } } { 3 }$

From momentum conservation, MV₁ = $\frac { \mathrm { M } } { 3 }$ V₂

From energy conservation V₁ = V₂/3

$\frac { 1 } { 2 }$ MV₁² + $\frac { 1 } { 2 }$ V₂²

= –

\ V₂ = $\sqrt { \frac { 3 \mathrm { gh } } { 4 } }$