# A certain force F applied to a particle of mass m1 gives it an acceleration of 4 m/s^2 and the same force when applied on mass m2 gives an acceleration of 3m/s^2. Two masses are held together and...

A certain force F applied to a particle of mass m1 gives it an acceleration of 4 m/s^2 and the same force when applied on mass m2 gives an acceleration of 3m/s^2. Two masses are held together and the same force is applied to the combination. Then what is the acceleration of the combination?

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A certain force F applied to a particle of mass m1 gives it an acceleration of 4 m/s^2 and the same force when applied on mass m2 gives an acceleration of 3 m/s^2.

If a force F is applied to a body of mass m, the resulting acceleration is a = F/m.

The acceleration of m1 when force F is applied is 4 m/s^2. This gives F/4 = m1. When the force F is applied to m2, the acceleration is 3 m/s^2. This gives F/3 = m2. If the masses m1 and m2 are held together and the force F is applied the acceleration is a = F/(m1+m2)

=> a = F/(F/3 + F/4)

= 1/(1/3 + 1/4)

= 1/(7/12)

= 12/7

The acceleration of the combined mass of m1 and m2 when force F is applied is 12/7 m/s^2