A ring of radius R = 4 m made of a highly dense material has a mass m1=5.4×109kg distributed uniformly over its circumference. A highly dense particle of mass m2=6×108kg is placed on the axis of the ring at a distance 3 m from the center of the ring. Find the speed of the particle (in cm/s), when the particle is at the center of the ring. Except mutual gravitational interaction of the two, neglect all other forces.
see full answer
Your Exam Success, Personally Taken Care Of
1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.
An Intiative by Sri Chaitanya
answer is 18.
(Unlock A.I Detailed Solution for FREE)
Best Courses for You
JEE
NEET
Foundation JEE
Foundation NEET
CBSE
Detailed Solution
When the particle is at the center, let their respective speedsare v1 and v2.From conservation of linear momentum, 0=5.4×109v1−6×108v2∴ v2=9v1From conservation of energy, (U+K)i=(U+K)f−Gm1m242+32+0=−Gm1m24+12m1v12+12m2v22Gm1m214−15=12m1v12+12m281v12G9m2220=1290m2v12∵m1=9 m2 Now m1=9m2 (given) v1=Gm2100=6.67×10−11×6×108100=0.02ms−1∴ v2=9v1=0.18ms−1=18cms−1
A ring of radius R = 4 m made of a highly dense material has a mass m1=5.4×109kg distributed uniformly over its circumference. A highly dense particle of mass m2=6×108kg is placed on the axis of the ring at a distance 3 m from the center of the ring. Find the speed of the particle (in cm/s), when the particle is at the center of the ring. Except mutual gravitational interaction of the two, neglect all other forces.