wiz-icon
MyQuestionIcon
MyQuestionIcon
4
You visited us 4 times! Enjoying our articles? Unlock Full Access!
Question

Three particles, each of mass m, are placed at the vertices of an equilateral triangle of side a. The net gravitational force on a body of mass M at the centroid of the triangle is


A

zero

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

GmMa2

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

2GmMa2

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

3GmMa2

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

The correct option is A

zero


Given that AB = BC = CA = a. The perpendiculars from A, B and C on opposite sides meet at the centroid O and bisect the sides AB, BC and CA. Let AO = BO = CO = r. Centroid also divides the lines AD, BE and CF in the ratio 2 : 1, i.e. AO=23AD, BO=23BE and CO=23CF.

In triangle ABD, AD=a sin 60=3a2
Similarly, BE = CF =3a2
r=AO=BO=CO=23×3a2=a3
The net force exerted on a unit mass placed at O due to three equal masses m at vertices A, B and C.

Since the three masses are equal and their distances from O are also equal, they exert forces FA, FB and FC of equal magnitude. Their directions are shown in the figure. It follows from the symmetry of forces that their resultant at point O is zero.


Hence, the correct choice is (a).


flag
Suggest Corrections
thumbs-up
8
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Torque
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon