A force produces an acceleration of `4m//s^(2)` in a body of `m_(1)kg` in another body of mass `m_(2)kg` If the same force is applied to `(m_(1) + m_(2))` then the acceleration will be

Options

A. `10m//s^(2)`
B. `2m//s^(2)`
C. `2.4m//s^(2)`
D. `5.4m//s^(2)`

Answer

c

Explanation

Here `a_(1) = 4m//s^(2) , a_(2) = 6m//s^(2)`
As force is same in all cases let it be `F`
`m_(1) = (F)/(a_(1)) = (F)/(4), m_(2) = (F)/(a_(2)) = (F)/(6)`
Total mass `= m_(1) + m_(2) = (F)/(4) + (F)/(6) = (5F)/(12)`
Same force is applied on the combination of masses.
`:. F = (m_(1) + m_(2))a` or `a = (F)/(m_(1) + m_(2)`
` a = (F xx 12)/(5F) = (12)/(5) = 2.4 m//s^(2)` .