Question

When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 25 kg, the acceleration of the object is 2 m/s^2. When the same force acts upon another object, its acceleration is 5 m/s^2 . What is the mass of this object?

Answer 1

Given:

mass of object, m = 25 kg

accelaration of the object, a = 2 m/
`s^(2)`

accelaration when force acts upon another object, a' = 5 m/
`s^(2)`

Step-by-step explanation:

To find the mass m' of the object:

Given that:

mass ∝
`(1)/(accelaration)`

Also, from Newton's second law of motion:

F = ma (1)

where,

F = force

Now, using eqn (1)

F =
`m* a`

F =
`25* 2` = 50 N

Now, since constant force acts on both the objects:

Therefore, F' =
`m'* a'` = F

50 =
`m'* 5`

m' = 10 kg

Therefore, the mass, m' of the second object is 10 kg