Two blocks of masses `m_(1)` and `m_(2)` are connected by an ideal sprit, of force constant `k`. The blocks are placed on smooth horizontal surface. A horizontal force `F` acts on the block `m_(1)`. Initially spring is relaxed, both the blocks are at rest.

What is maximum elongation of spring.

Options

A. `(2m_(1)F)/((m_(1)+m_(2))k)`
B. `(m_(1)^(2)F)/(2(m_(1)+m_(2))k)`
C. `(2m_(2)F)/(k(m_(1)+m_(2)))`
D. `(m_(2)^(2)F)/(2(m_(1)+m_(2))^(2)k`

Answer

C

Explanation

`x_(1)+x_(2)=x` ………..i
`(F-m_(1)a_(cm))x_(1)+m_(2)a_(cm).x_(2)-1/2kx^(2)=0`…….ii
where `a_(cm)=F/(m_(1)+m_(2))`………….iii
solve get answer.