Question

The escape velocity of an object of mass M from the surface of earth is v m/s. Then the value of escape velocity of a mass 2M from a planet of diameter 4 times that of earth is :

• A. √2v m/s
• B. v m/s
• C. v/2m/s
• D. 4 v m/s

Answer 1

Answer:

C. v/2m/s

• The escape velocity ($v_e$) of an object from the surface of a planet depends only on the mass of the planet and its radius, not on the mass of the escaping object:v_e=(2GM_p/R_P)^1/2

• Diameter of the planet = 4 X Diameter o f Earth

• Therefore, Radius of the planet R' = 4 R_E

• Now, calculated for the new planet:V^'=(2GM_p/R^')^1/2=(2GM_E/4R^'_E)^1/2=V/2

• Thus, the escape velocity of a mass $2M$ from this planet isV/2m/s