wiz-icon
MyQuestionIcon
MyQuestionIcon
3
You visited us 3 times! Enjoying our articles? Unlock Full Access!
Question

A rocket is launched vertically from the surface of the earth of radius R with an initial speed v. If atmospheric resistance is neglected, the maximum height attained by the rocket is given by


A

h=R(2gRv21)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

h=R(2gRv2+1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

h=R(2gRv21)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

h=R(2gRv2+1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A

h=R(2gRv21)


On the surface of the earth, the total energy is
KEi+PEi=12mv2GmMR
where m is the mass of the rocket and M that of the earth. At the highest point, v = 0 and the energy is entirely potential.
PEf=GmM(R+h) where h is the maximum height attained.
From the law of conservation of energy, we have
12mv2GmMR=GmM(R+h)
R+hh=2gRv2(g=GMR2)
h=R(2gRv21)
Hence, the correct choice is (a).


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Gravitational Potential Energy Tackle
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon