A system consists of two cubes of mass `m_(1)`, and `m_(2)` respectively connected by a spring of force constant k. force (F) that should be applied to the upper cube for which the lower one just lifts after the force is removed, is

Options

A. mg
B. `m_(2)g`
C. `(m_(1)+m_(2))g`
D. `(m_(1)m_(2))/(m_(1)+m_(2))g`

Answer

C

Explanation

Let `x_(0)` be the maximum compression, then
`m_(1)g+F=kx_(0)" "...(i)`
`"and "(1)/(2)kx_(0)^(2)=m_(1)gx_(0)" "...(ii)`
If x is the maximum elongation, then
`kx = m_(2)g" "...(iii)`
`"and "-(1)/(2)kx^(2)=m_(1)g(x
+x_(0))" "...(iv)`
`"or "k(x_(0)-x)=2m_(1)g`
From Eqs. (i) and (iii), we get
`m_(1) g+ F- m_(2)g = k (x_(0) -x) =2m_(1)g`
`"or "F = 2m_(1)g + m_(2) g-m_(1)g=(m_(1)+m_(2))g`