When a constant force is applied to an object, the acceleration of the object yaries inversely with its mass. When a certain constant force acts upon an object with mass 6 kg the acceleration of the object is 13m/s^2 When the same force acts upon another object,its acceleration is 3m/s^2 . What is the mass of this object? square

To solve this problem, we can use the concept of inverse variation. According to the problem, the acceleration of an object varies inversely with its mass when a constant force is applied.<br /><br />Let's denote the mass of the first object as \( m_1 \) and its acceleration as \( a_1 \). Similarly, let's denote the mass of the second object as \( m_2 \) and its acceleration as \( a_2 \).<br /><br />Given:<br />- \( m_1 = 6 \) kg<br />- \( a_1 = 13 \) m/s²<br />- \( a_2 = 3 \) m/s²<br /><br />Since acceleration varies inversely with mass, we have the relationship:<br />\[ m_1 \cdot a_1 = m_2 \cdot a_2 \]<br /><br />Now, we can solve for \( m_2 \):<br />\[ m_2 = \frac{m_1 \cdot a_1}{a_2} \]<br /><br />Substitute the given values:<br />\[ m_2 = \frac{6 \, \text{kg} \cdot 13 \, \text{m/s}^2}{3 \, \text{m/s}^2} \]<br /><br />Calculate the value:<br />\[ m_2 = \frac{78 \, \text{kg} \cdot \text{m/s}^2}{3 \, \text{m/s}^2} \]<br />\[ m_2 = 26 \, \text{kg} \]<br /><br />Therefore, the mass of the second object is \( 26 \) kg.