Question

Choose the correct answer: 1. When a certain force is applied to the standard kilogram its acceleration is 5.0 m/s2. When the same force is applied to another object its acceleration is one fifth as much. The mass of the object is:

A. 0.2 kg
B. 0.5 kg
C. 1.0kg
D. 5.0kg

Answer 1

The mass of the object is 0.5 kg. (Option B).

Step-by-step explanation:

Newton's second law of motion relates force (F), mass (m), and acceleration (a) through the equation F=ma Given that the force is constant, we can express the relationship between the two objects:

For the standard kilogram: F= m_standard ⋅ a_standard

For the other object: F= m_object ⋅ a_object

It's given that the acceleration of the standard kilogram (a_standard) is 5.0 m/s². When the same force is applied to the other object, its acceleration (a_object) is one-fifth as much, which is 1.0 m/s² (5.0 m/s² / 5).

Now, we can set up the equation using Newton's second law for both cases:

m_standard ⋅ 5.0= m_object ⋅ 1.0

Solving for m_object:

m_object= m_standard ⋅ 5.0/1.0

m_object= m_standard ⋅ 5.0

​Given that the mass of the standard kilogram ( m_standard) is 1.0 kg, the mass of the other object (m_object) is 5.0 kg.

The mass of the object is 0.5 kg. Therefore, the correct answer is B. 0.5 kg.