A mass of $M$ at rest is broken into two pieces having masses $m$ and $(M - m)$ . The two masses are then separated by a distance. The gravitational force between them will be the maximum when the ratio of the masses [ $m : (M - m)$ ] of the two parts is:

1 : 1

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

1 : 2

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

1 : 3

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

1 : 4

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

Open in App

Solution

The correct option is A $1 : 1$
The gravitational force between two masses
$F = \frac{G m_{1} m_{2}}{r}$
$m_{1} = m$
$m_{2} = (M - m)$
$∴ F = \frac{G m (M - m)}{r^{2}}$
For maximum gravitational force, $\frac{d F}{d m} = 0$
$∴ \frac{d}{d m} [m (M - m)] = 0$
By solving we get $m = \frac{M}{2}$
So, $\frac{m}{M - m} = \frac{1}{1}$

Suggest Corrections

Similar questions

A mass M is split into two parts, m and (M-m), which are then separated by a certain distance. What ratio of $\frac{m}{M}$ maximizes the gravitational force between the two parts

Q. If mass M is split into two parts, m and

(M - m)

which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts.

Q. A mass M is split into two parts (M-m) and m, which are then separated by a distance r. For what ratio of m/M, will gravitational attraction between them be maximum:

Q. Mass

m

is divided into two parts

X m

and

(1 - X) m

. For a given separation, the value of

X

for which the gravitational force of attraction between the two pieces becomes maximum is :

Mass M is divided into two parts m1and m2.fr a given separation the ratio of m1/M forwhich the gravitational attraction between the two parts becomes maximum is

1:1

1:2

1:3

1:4

Ans option 2 how?

Join BYJU'S Learning Program

A mass of M at rest is broken into two pieces having masses m and (M−m). The two masses are then separated by a distance. The gravitational force between them will be the maximum when the ratio of the masses [m:(M−m)] of the two parts is:

The correct option is A 1:1The gravitational force between two massesF=Gm1m2rm1=mm2=(M−m)∴F=Gm(M−m)r2For maximum gravitational force, dFdm=0∴ddm[m(M−m)]=0By solving we get m=M2So, mM−m=11

A mass of $M$ at rest is broken into two pieces having masses $m$ and $(M - m)$ . The two masses are then separated by a distance. The gravitational force between them will be the maximum when the ratio of the masses [ $m : (M - m)$ ] of the two parts is: