Mass M is divided into two parts xm and (1-x)m . For a given separation the value of x for which the gravitational attraction between the two pieces becomes maximum is

Options

A. `1/2`
B. `3/5`
C. 1
D. 2

Answer

A

Explanation

According to Newton's Law of gravitation ,
f`alpha m_1M_2`
`F= m_1M_2K(xm)(1-x)m`
For F to be maximum `(df)/(dx) = 0`
`(d)/ (dx) (k(xm) (1-x)m) = 0` `Rightarrow (d)/(dx)[ m^2x-x^2m^2]` =0
`Rightarrow m^2-2xm^2`= 0
`m^2= 2xm^2`
`therefore x= (1)/(2)`