The correct option is B 3 m
The acceleration due to gravity at the surface of a planet is given by
g=GMR2⇒g=GR2×43πR3ρ [∵M=43πR3ρ]
⇒g=43πGρR
Hence,g∝ρRLet, gm be the accelaration due to gravity at the surface of the moon and ge the accelaration due to gravity at the surface of the earth.
⇒gmge=ρmρeRmRe
According to the given problem,
ρmρe=23 and RmRe=14
⇒gmge=(23)(14)
⇒gm=ge6
Since the astronaut has energy to jump only upto he=0.5 m on earth which will be equal to the work done by him to jump 0.5 m.
Since, he will do the same work on the both Earth and planet. So,
mgehe=mgphp
Substituting the values, in the above equation we get,
ge×0.5=ge6×hp
∴hp=3 m
Hence, option (b) is correct answer.