wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Two rings having masses M and 2M, respectively, having the same radius are placed coaxially as shown in the figure. If the mass distribution on both the rings is non-uniform, then the gravitational potential at point P is


A
Zero
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
GMR[1225]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
GMR[1+12]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
GMR[12+25]
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D GMR[12+25]
Given that,
Mass of left ring =M
Mass of the right ring =2M
The radius of each ring =R

As all the points on the periphery of either ring are at the same distance from point P. The potential at point P due to the whole ring can be calculated as
V=GMR2+x2
where x is the axial distance from the centre of the ring and G is the gravitational constant.

This expression is independent of the fact of whether the distribution of mass is uniform or non-uniform.

Axial distance of point P from left ring =R
Axial distance of point P from right ring =3RR=2R
The gravitational potential at P due to both the rings is
Vnet=GMR2+R2G×2MR2+(2R2)
Vnet=GM2RG×2M5R
Vnet=GMR[12+25]

Hence, option (a) is correct.
Why this question?
Note: Even though the ring has non-uniform mass distribution, the potential expression remains the same. This is because potential is a scalar quantity and all points on the ring are equidistant from the point on the axis.

Key Concept: The gravitational potential due to a ring on its axis is given by V=GMR2+x2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon