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Question

A system consists of two cubes of masses m1 and m2 respectively connected by a spring of force constant k. The force (F) that should be applied to the upper cube for which the lower one just lifts after the force is removed, is


A
m1g
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B
m2g
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C
(m1+m2)g
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D
m1+m2m1+m2g
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Solution

The correct option is D (m1+m2)g
Initially in equilibrium
F+m1g=kxi           (xi=initial compression)
      xi=F+m1gk          ...(1)
Let xf be the elongation in spring when lower block just lifts.  Then,
 kxf=m2g    or   xf=m2gk     ....(2)
Now from conservation of mechanical energy, increase in gravitational potential energy of m1 = decrease in elastic potential energy of spring.
    m1g(xi+xf)=12k(x2ix2f)
substituting the values of xi and xf from Eqs. (1) and (2), we get
F=(m1+m2)g

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