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 objectwith mass 2 kg, the acceleration of the object is 10 m/s². When th same force acts upon another object, its acceleration is 4 mm/s. What is the mass of thisobject?

Answer 1

The mass of this object will now be 5kg

Answer 2

Given:

The acceleration varies inversely with its mass.

When:

mass = 2 kg, the acceleration = 10 m/s²

Let's find the mass when the acceleration is 4 m/s².

Since the acceleration of the object varies inversely with its mass, we have the equation:

`a=(k)/(m)`

Where:

a is the acceleration

m is the mass

k is the constant of variation.

When m = 2, a = 10:

`10=(k)/(2)`

Now, let's find k.

Multiply both sides by 2

`\begin{gathered} 10*2=(k)/(2)*2 \\ \\ 20=k \\ \\ k=20 \end{gathered}`

Now, the equation which represents this variation is:

`a=(20)/(m)`

Now, to find the mass when acceleration is 4 m/s², substitute 4 for a and solve for m.

We have:

`\begin{gathered} 4=(20)/(m) \\ \\ m=(20)/(4) \\ \\ m=5 \end{gathered}`

Therefore, when the acceleration is 4 m/s², the mass of the object is 5 kg.

• ANSWER:

5 kg