Two blocks (1 and 2) of equal mass m are connected by an ideal string (see figure shown) over a frictionless pulley. The blocks are attached to the ground by springs having spring constants `k_(1)` and `k_(2)` such that `k_(1) gt k_(2)`

Initially, both springs are unstretched. The block 1 is slowly pulled down a distance x and released. Just after the release the possible values of the magnitude of the acceleration of the blocks `a_(1)` and `a_(2)` can be–

Options

A. Either `(a_(1) = a_(2) = ((k_(1) + k_(2)))/(2m)) or (a_(1)= (k_(1)X)/(m) - g)` and `(a_(2) = (k_(3)x)/(m)+g)`
B. `(a_(1) = a_(2) = ((K_(1) + k_(2))x)/(2m))` Only
C. `(a_(1) = a_(2) = ((k_(1)-k_(2))x)/(2m))`Only
D. Either `(a_(1) = a_(2) ((K_(1) - k_(2)))/(2m)) or (a_(1)= a_(2) ((k_(1)k_(2)))/((k_(1) + k_(2))m) -g)`

Answer

B

Explanation

When block 1 is slowly pulled down as distance x and released

`k_(1) x - mg = ma_(1) " " …….(i)`
`rArr a_(1) = (k_(1)x)/(m) - g`
`k_(2)x + mg = ma_(2) " "………..(ii)`
if `a_(1) = a_(2)`, then add equation (i) + (ii)
`2ma = k_(1) x + k_(2)x`
`rArr a = a_(1) = a_(2) = ((k_(1) + k_(2))x)/(2m)`