A block is hanged from spring in a cage. Elongation in spring is x 1 and x 2 when the cage moves up and down respectively with the same acceleration. The expansion in spring when the cage move horizontally with the same acceleration -

Step-by-step solution

Elongation in spring is given by x = m k ( g e f f ) When the cage is moving up by acceleration a x 1 = m k ( g + a ) When the cage is moving down with acceleration a x 2 = m k g - a When the cage is moving with acceleration a horizontally x 3 = m k g 2 + a 2 m = m a s s   o f   p e n d u l u m   k = s p r i n g   c o n s t a n t u s i n g   1 2 + 2 2 ∴ x 1 2 + x 2 2 = m 2 k 2 . 2 ( g 2 + a 2 ) = 2 x 3 2 ⇒   x 3 = x 1 2 + x 2 2 2