For configuration (i), gravitational force on
M due to
m and
m
F1=+= [1+] =. ........(i)
For configuration (ii), gravitational force on
M due to
m and
m
F2=−=0 ........(ii)
For configuration (iii), gravitational force on
M
F3=√(F′)2+(F")2 (∵ angle between
F′ and
F" is
90° )
=√()2+()2 =√2 .........(iii)
For configuration (iv), gravitational force on
M, where
0<θ<90°
F4=√(F′)2+(F")2+2F′F"cosθ =√()2+()2 +2.cosθ =√1+1+2cosθ =√2(1+cosθ) =(√2)√1+cosθ ..........(iv)
(∵ for
0<θ<90°,√1+cosθ>) From Eqs. (i), (ii), (iii) and (iv), we get
F2<F1<F3<F4 Thus, the correct option is (b).