Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

Gravitational acceleration on the surface of a planet is 611g, where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is 23 times that of the earth. If the escape speed on the surface of earth is taken to be 11kms1 what will be the escape speed on the surface of this planet?

Answer
VerifiedVerified
497.4k+ views
like imagedislike image
Hint: The gravitational force is defined as the force which acts between two masses. It is always attractive.Escape speed of a moving body is the minimum speed required to escape from the gravitational field of a planet and move into space.We use the relation of gravitational acceleration and escape velocity to obtain the escape velocity on the planet.
Formula used:
Acceleration due to gravity on the surface of a planet is gp=GMPRp2 and,the escape velocity from the surface of the planet is vp=2GMpRp

Complete answer:
Acceleration due to gravity is the acceleration of the object due to gravitational force of a planet.
Acceleration due to gravity on a planet of mass Mp and radius Rp is given by relation
gp=GMPRp2 where G is the gravitational constant
The escape velocity of an object from the surface of the planet is
vp=2GMpRp
Mass density is defined as volumetric mass and given by
ρ=mV where m and V denotes mass and volume of the material respectively.
Assuming a planet to be spherical, its mass density can be given as
ρp=Mp43πRp3
Substituting this in (1) and rearranging, we get
Rp=3gp4πGρp
Now we substitute this value in (2) and get
vp=3gp22πGρp
Similarly acceleration due to gravity of earth is given by’
ve=3ge22πGρe
Taking ratio of vp and ve and substituting the given values; we get
vpve=(gp/ge)2ρp/ρe=(6/11)22/3
vp=(6/121)2/3ve=311×11km/s
vp=3km/s
We conclude that escape velocity on the planet is 3 km /s.

Note:
Escape velocity is the minimum speed required to get out from the gravitational field of the planet. Escape velocity is independent of mass of the object. It depends on the radius of the planet and acceleration due to gravitational force of the planet.
Escape velocity on the surface of the earth is 11.2 km/s.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
ChemistryChemistry
MathsMaths
₹41,848 per year
Select and buy