CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

Two spherical bodies of mass M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is:

A
7.5R
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
1.5R
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2.5R
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4.5R
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 7.5R

Assuming velocities of masses M and 5M are v1 and v2 respectively
Using conservation of momentum principle
Mv1+5Mv2=0v2=v15...(i)
Using energy conservation principle
ΔP.E.=ΔK.E.
The P.E. is given as Gm1m2r
G5M212R(G5M23R)=12Mv21+125Mv220
from equation (i) substituting value of v2
15GM212R=12Mv21+125M(v15)2
G5M24R=12Mv21+12Mv215
12Mv21=K.E. of mass M just before collision =25GM224R
Using work energy theorem:
work done by gravitational force =ΔK.E.
r12RF.dr=12mv1
r12RGM5Mr2dr=12mv1
[GM5Mr]r12R=12mv1
GM5M(1r112R)=25GM224R
r=7.5R
hence correct answer is option A


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
The Law of Conservation of Mechanical Energy
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon