Question

Let the escape velocity of earth be V. If a planet which has same mass density as earth and radius half to that of earth. The escape velocity will be:

• A. V
• B. 0.5 V
• C. 2 V
• D. None of these

Answer 1

The correct option is B 0.5 V

The escape Velocity, Vof a planet is given by: V = $\sqrt{\frac{2GM}{R}}$
where, G $\to$ Universal Gravitational constant
M $\to$ Mass of the planet
R $\to$ Radius of the planet
For new planet, R (planet)$\frac{M}{8}(forM\to MassofEarth)$
So, Volume (planet) = $\frac{V_o}{8}$ ( for $V_o\to$ Volume of earth)
Which gives, M (planet) = $\frac{M}{8}(forM\to Volumeofearth)$
Putting values, (with G being the same); we get:
V (planet) = $\frac{V\left(earth\right)}{2}$
or, V (planet) = 0.5 V (earth)