A force of `5N` gives a mass `m_(1)`, an acceleration of `8 m//s^(2)`, and a mass `m_(2)`, an acceleration of `24 m//s^(2)`. What acceleration would it give if both the masses are tied together?

Explanation

(i) In the first case:
Force, F=5 N
Mass,m=`m_(1)` (To be calculated)
And, Acceleration, a = 8 m/`s^(2)`
Now, F=`mxxa`
So, `5=m_(1)xx8`
And, `m_(1)=5/8kg`
`m_(1)=0.625kg`
Thus, the mass `m_(1)` is 0.625 kg.
(ii) In the second case:
Force, F = 5 N
Mass, m=`m_(2)` (To be calculated)
And, Acceleration a=24 m/`s^(2)`
Now, F=m`xx`a
So, `5=m_(2)xx24`
And, `m_(2)=5/24kg`
`m_(2)=0.208` kg
Thus, the mass m2 is 0.208 kg.
(iii) In the third case:
Force=5N
Total mass, m = `m_(1)+m_(2)`.
=0.625+0.208
=0.833 kg
And, Acceleration, a = ? (To be calculated)
Now putting these values in the relation :
`F=mxxa`
We get : `5=0.833xxa`
`a=5/0.833`
`a=6 m//s^(2)`
Thus, if both the masses are tied together, then the acceleration would be 6 m/`s^(2)`