wiz-icon
MyQuestionIcon
MyQuestionIcon
5
You visited us 5 times! Enjoying our articles? Unlock Full Access!
Question

A planet of mass M, has two natural satellites with masses m1 and m2. The radii of their circular orbits are R1 and R2 respectively. Ignore the gravitational force between the satellites. Define v1,L1,K1 and T1 to be respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and v2,L2,K2 and T2 to be the corresponding quantities of satellite 2. Given m1/m2=2 and R1/R2=1/4, match the ratios in List - I to the numbers in List-II.

List - IList - II
P. v1v21. 18
Q. L1L22. 1
R. K1K23. 2
S. T1T24. 8

A
P4;Q2;R1;S3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
P3;Q2;R4;S1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
P2;Q3;R1;S4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
P2;Q3;R4;S1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is D P3;Q2;R4;S1

GMm1R21 = m1v21R1

v21=GMR1,v22=GMR2

v21v22=R2R1=4

(P) v1v2=2

(Q) L = mvR

L1L2=m1v1R1m2v2R2=2×2×14=1

(R) K = 12mv2

K1K2=m1v21m2v22=2×(2)2=8

(S) T = 2πR/v

T1T2=R1v1×v2R2=R1R2×v2v1=14×12=18



flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Orbital Velocity
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon