Question

A force produces an acceleration of 1 a in a body and same force produces an acceleration of 2 a in another body. If the two bodies are combined and the same force is applied on the combination, the acceleration produced in it is​

Answer 1

The equivalent mass m = m1+m2. Newton's second law states that acceleration produced in the body of mass m is directly proportional to force applied and inversely to the mass of the body.

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Answer 2

Answer:

$a = \dfrac{a_1a_2}{a_1+a_2}$

Explanation:

Let us assume two bodies having masses m₁ and m₂ and F be the force which is applied on the bodies separately.

We know that according to Newton’s second law of motion:

F=ma. (1)

Now on applying this on body of mass m₁, we have:

$F = m_1a_1$

On dividing both sides by a₁, we get:

$m_1 = \dfrac{F}{a_1} \ \ (2)$

Now on applying this on body of mass m₂, we have:

F = m₂a₂

On dividing both sides by a₂, we get:

$m_2 = \dfrac{F}{a_2} \ \ (3)$

The equivalent mass m = m₁+m₂

Now on applying equation 1 on this equivalent mass, we have:

F = (m₁+m₂)a

a = acceleration on combination

On dividing both sides by m₁+m₂, we get:

$a = \dfrac{F}{m_1+m_2}$

Putting the value of m1 and m2in above equation, we get :

$a = \dfrac{F}{\dfrac{F}{a_1}+\dfrac{F}{a_2}}$

$a = \dfrac{\bcancel{F}}{\bcancel{F}\bigg(\dfrac{1}{a_1}+\dfrac{1}{a_2}\bigg)}$

$a = \dfrac{a_1a_2}{a_1+a_2}$

$\therefore \underline{\boxed{a = \dfrac{a_1a_2}{a_1+a_2}}}$

Hope it helps!!