Question

a force produces an acceleration a on body A and 3a on body B. Calculate the acceleration produced of same force is applied on a combined mass A and B​

Answer 1

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Answer 2

The acceleration produced when same force is applied on the combined mass = 3a/4

Let the force applied on the bodies be F.

m1 - mass of body A

m2 - mass of body B

Given that acceleration of A = a and acceleration of B = 3a . Let acceleration of the combined mass be a'.

Force = mass × acceleration

For body A-

F = m1 × a

=> m1 = F/a

For body B-

F = m2 × 3a

=> m2 = F/3a

For the combined mass(m1 + m2) -

F = (m1 + m2) a'

=> a' = F / (m1 + m2)

=> a' = F / (F/a + F/3a) [ m1 = F/a , m2 = F/3a ]

=> a' = a/(1+1/3)

=> a' = 3a/4

The acceleration of combined mass = 3a/4