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
• B. $\frac { \mathrm { m } _ { 1 } \mathrm {~m} _ { 2 } } { \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } } \mathrm {~g}$
• C. (m₁ + m₂) g
• D. m₂g

Answer 1

Answer: (C)

(m₁ + m₂) g

Answer 2

Initially, F = m₁g = k₁x₁

x₁ = $\frac { \mathrm { F } + \mathrm { m } _ { 2 } \mathrm {~g} } { \mathrm { k } }$ ....(1)

Finally x₂ = $\frac { \mathrm { m } _ { 2 } \mathrm {~g} } { \mathrm { k } }$ .... (2)

From conservation of energy,

m₁g(x₁ + x₂) = $\frac { 1 } { 2 }$ k $\left( x _ { 1 } ^ { 2 } - x _ { 2 } ^ { 2 } \right)$ .... (3)

From (1), (2) & (3), F = (m₁ + m₂)g