A force of 100 N gives a mass m1, an acceleration of 10 ms⁻² and of 20 ms⁻² to a mass m₂. What acceleration must be given to it if both the masses are tied together?

Suppose, a = acceleration produced if m₁ and m₂ are tied together,
F = 100 N
Let a₁ and a₂ be the acceleration produced in m₁ and m₂, respectively.
a₁ = 10 ms⁻², a₂ = 20 ms⁻² (given)
Again m₁ = F/a₁ and m₂ = F/ a₂
m₁ = 100/10 = 10 ms⁻²
and m₂ = 100/20 = 5 ms⁻²
m₁ + m₂ = 10 + 5 = 15
So, a = F/m₁ + m₂ = 100/15 = 20/3
= 6.67 ms⁻²