Force F depends on distance \(x\) and time \(t\) as \(F = ax^ 2 + bt\;\frac{1}{2}\) . Final dimension of \(\frac{b^2}{a}\) is
- \(M^{ - 1} L^2 T^{-3}\)
- \(M ^1 L^{ -3} T^3\)
- \(M^ 1 L^3 T^{-3}\)
- \(M ^2 L^ 2 T^1\)
The Correct Option is C
Solution and Explanation
The Correct Option is (C) : \(M^ 1 L^3 T^{-3}\)
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Concepts Used:
Forces
A force is a physical influence that can cause an object to change its motion or shape. Forces can be classified into two broad categories: contact forces and non-contact forces.
Contact forces arise from direct physical contact between two objects. Examples of contact forces include friction, tension, normal force, and air resistance.
Non-contact forces, also known as field forces, act at a distance and do not involve physical contact between objects. Examples of non-contact forces include gravitational force, electric force, and magnetic force.
Forces can be described in terms of their magnitude, direction, and point of application. The magnitude of a force is typically measured in units of newtons (N), and the direction is specified using vectors.
The effects of forces can be described using Newton's laws of motion. Newton's first law states that an object at rest will remain at rest, and an object in motion will continue to move at a constant velocity unless acted upon by an unbalanced force. Newton's second law relates the force applied to an object to its resulting acceleration, and Newton's third law states that for every action, there is an equal and opposite reaction.
Forces play a fundamental role in many branches of physics, including mechanics, electromagnetism, and thermodynamics. They are essential to understanding the behavior of physical systems and are important in applications such as engineering, medicine, and space exploration.