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What property of an object determines how much inertia it has?

Answer
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Hint: You could recall Newton's first law of motion which is also called the law of inertia as this law introduces the concept of inertia. From the law you will understand that the inertia is fundamentally the restriction to the motion and thus determine the property that is asked in the question.

Complete solution:
You may recall Newton’s first law of motion. This law states that a body tends to stay in the state of rest or of uniform motion, until and unless it is provided with an external force. So we could conclude that every object has a property that resists any change in their state of motion. This tendency is termed as ‘inertia’.

Now you may wonder whether every object shows this property uniformly. You should understand this fact that this property, that is, the inertia shows variation with mass. The more massive an object is the more the inertia of that object will be.

We could also make another conclusion that the more inertia a body has the more massive that body is.

You could take two blocks of different masses and then place them on a table. Then you could give a push to both the blocks in equal magnitude then, the more easily a block moves the less inertia that block has and lower will be its mass.

Therefore, we found that the mass is the property of an object that determines how much inertia it has.

Note:
Its common misconception among the non-scientific community that a force is always required for moving an object. But actually, the force can even cause the object to come to rest. You could think about the case of frictional force, this force actually restricts the relative motion between two bodies.