Figure shows the acceleration of objects of different mass that experience the same force. What is the magnitude of the force?

Here acceleration of different objects vs mass of different objects graph is given which feel the same force then find the magnitude of the force.

To find the force magnitude use the Newton second law

newton second law say that force is directly proportional to acceleration.

$F=ma.......\left(1\right)$

consider mass of the object is 100 g means 0.1 kg and acceleration is 15 m/s²

substitute the value of mass and acceleration in equation (1) to find force

$$\begin{gathered} F_1=m_1{a}_1 \\ {F}_1=0.1kg\times 15m/s^2 \\ {F}_1=1.5N......\left(2\right) \end{gathered}$$

consider mass of the object is 300 g means 0.3 kg and acceleration is 5 m/s²

substitute the value of mass and acceleration in equation (1) to find force

substitute the value of equation (2) and (3) to find magnitude of the force

$$\begin{gathered} F=\sqrt{F_1^2+F_2^2} \\ F=\sqrt{{\left(1.5\right)}^2+{\left(1.5\right)}^2}N \\ F=\sqrt{2.25+2.25}N \\ F=\sqrt{4.5}N \\ F=2.12N \end{gathered}$$