Infinite number of masses, each of mass m, are placed along a straight line at distance of r, 2r, 4r, 8r, etc. from a reference point O

\frac{5 G m}{4 r^{2}}

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

\frac{4 G m}{3 r^{2}}

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

\frac{3 G m}{2 r^{2}}

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

\frac{2 G m}{r^{2}}

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

Open in App

Solution

The correct option is B $\frac{4 G m}{3 r^{2}}$
$I = G m [\frac{1}{r^{2}} + \frac{1}{(2 r^{2})} + \frac{1}{(4 r^{2})} + \dots]$

$= \frac{G m}{r^{2}} [1 + \frac{1}{2^{2}} + \frac{1}{4^{2}} + \frac{1}{8^{2}} + \dots]$

$= \frac{G m}{r^{2}} \frac{4}{3} = \frac{4}{3 r^{2}} G m$

Suggest Corrections

Similar questions

Particles of mass 2 gm, 3 gm, 5 gm and 6 gm are placed at the points (-6, 1), (5, 0), (-3, 2) and (2, -2) respectively. The co-ordinates of the centre of mass of the system will be

Q. The set of real numbers r satisfying

\frac{3 r^{2} - 8 r + 5}{4 r^{2} - 3 r + 7} > 0

An object is propelled vertically to a maximum height of 4R from the surface of a planet of radius R and mass M. The speed of object when it returns to the surface of the planet is

Q. Two bodies of masses

m

and

4 m

are placed at a distance

r

. The gravitational potential at a point on the line joining them where the gravitational field is zero, is

Q. Two stars of masses m & 3m are released. The initial distance between them is r. Find the speed of approach when distance between them decreases to

\frac{r}{2}

Join BYJU'S Learning Program

Infinite number of masses, each of mass m, are placed along a straight line at distance of r, 2r, 4r, 8r, etc. from a reference point O

The correct option is B 4Gm3r2I=Gm[1r2+1(2r2)+1(4r2)+⋯] =Gmr2[1+122+142+182+⋯] =Gmr243=43r2Gm

The correct option is B $\frac{4 G m}{3 r^{2}}$
$I = G m [\frac{1}{r^{2}} + \frac{1}{(2 r^{2})} + \frac{1}{(4 r^{2})} + \dots]$

$= \frac{G m}{r^{2}} [1 + \frac{1}{2^{2}} + \frac{1}{4^{2}} + \frac{1}{8^{2}} + \dots]$

$= \frac{G m}{r^{2}} \frac{4}{3} = \frac{4}{3 r^{2}} G m$