What height weight of object is 1/3rd of weight at surface of earth. (1) R (2) 2R (3)(√3-1)R (4) (5-1)R

Question

What height weight of object is \(\frac13\)rd of weight at surface of earth. 

(1) R

(2) 2R

(3) (√3-1)R

(4) (√5-1)R

Answer 1

Correct option is (3) (√3-1)R

\(g^1 = \frac g{\left(1 + \frac hR\right)^2}\)

\(\frac13 = \frac1 {\left(1 + \frac gR \right)^2}\)

\(1 +\frac hR = \sqrt 3\)

\(h = (\sqrt 3 - 1)R\)