A force applied on a body is represented as

Force is a vector quantity, meaning it possesses both magnitude and direction. In physics, vectors are often represented using unit vector notation (i, j, k) to denote components along the x, y, and z axes respectively. Option 2, '10j + 2 kg' (interpreted as 10j + 2i or a similar vector form), represents a force vector. While the SI unit of force is the newton (N), which is equivalent to kg·m/s² [1], force is fundamentally the product of mass and acceleration (F=ma) [2]. In some contexts, particularly in engineering or older texts, 'kg' is colloquially used to refer to 'kilogram-force' (kgf), where 1 kgf is the force exerted by gravity on a 1 kg mass [2]. Given the options, only the second choice provides a vector representation suitable for a force applied on a body, whereas the others are either scalars or lack units.

Sources

1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > 5.3 Are Forces an Interaction Between Two or More Objects? > p. 65
2. [2] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > 5.5 Weight and Its Measurement > p. 72