Question

A force of 5 N gives a mass m₁ , an acceleration of 8 m/s² , and a mass of m₂ , an acceleration of 24m/s².
What acceleration would it give if the both the masses are tied together ?

Answer 1

Force= Mass × Acceleration

Considering the first case

CASE-1
Force=5 N
acceleration=8 ms⁻²
From the above formula:
5=m₁ × 8
m₁=5/8 kg

CASE-2
Force=5 N
Acceleration= 24ms⁻²

5=m₂ × 24
m₂=5/24 kg

Now to the question:
What if both the masses are tied together [considering the rope used is weightless]

CASE-3
Force=5 N
mass=m₁+m₂=5/8 +5/24 = 0.6250 +0.2083 = 0.8333

Force=mass × acceleration
acceleration= Force/Mass
                    =5/0.8333
                    =6.00024 m⁻²   ≈ 6 ms⁻²