Question

Statement-1 : Th escape valocity from the earth is `upsilon_(e)`. Th esacpe velocity from a planet whose radius to twice that of the earth and mean density is same as that of the earth is `2 upsilon_(e)`.
Statement-2 : `upsilon_(e) = sqrt(g R)`
A. Statement -1 is true , Statement -2 is true , Statement-2 is a correct explanation of Statement -1.
B. Statement -1 is true , Statement-2 is true , Statement-2 is a correct explanation of Statement-1.
C. Statement-1 is true , Statement-2 is false.
D. Statement-1 is false , Statement-2 is true.

Answer 1

Correct Answer - C
Here, statement-1 is correct but statement-2 is wrong
As `upsilon_(e) = sqrt((2GM)/(R )) = sqrt((2G)/(R ) xx (4)/(3) pi R^(3) rho)`
so `upsilon_(e) prop R`
`:. (upsilon_(p))/(upsilon_(e)) = (2R)/(R ) = 2`
or `upsilon_(p) = 2upsilon_(e)`