Question:

The force $F$ is given by expression $F=A \cos (B x)+C \sin (D t)$, where $x$ is the displacement and $t$ is the time. Then dimension of $\frac{D}{B}$ are same as that of

Updated On: Jul 29, 2022
  • velocity $[LT^{-1}]$
  • angular velocity $[T^{-1}]$
  • angular momentum $[ML^2T^{-1}]$
  • velocity gradient $[T^{-1}]$
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The Correct Option is A

Solution and Explanation

In trigonometric function like $\sin \,\theta, \cos \,\theta$ etc $\theta$ is dimensionless So, $\left.[B x]= M ^{0} L^{0} T^{0}\right]$ $[B]=\left[ L ^{-1}\right]$ Also, $[Dt] = [M^0L^0T^0]$ $[D] = [T^{-1}]$ Now $\left[\frac{D}{B}\right]=\left[ LT ^{-1}\right]$
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Concepts Used:

Types of Forces

Different types of forces that are found in nature can be broadly categorized into two types: 

  1. Contact Force
  2. Action-at-a-distance Force

Contact Force

Contact Forces can further be divided into the following types: 

  • Applied Force: It is the force that one object exerts on the other object directly. For example, pushing a door, hitting a ball with a hockey stick, opening a drawer, etc.
  • Frictional Force: Frictional Force is a type of Contact Force that opposes the movement of an object on a surface. In other words, it is a resisting force. For example, a ball rolling on a floor slows down and eventually stops, applying brakes to stop a vehicle, writing on a notebook, etc. Frictional Force is of two types: Static Friction and Dynamic Friction.
  • Air Resistance Force: Just like a surface opposes the movement of an object, the air opposes the objects moving through it. This type of force is called the Air Resistance Force. The strength of the Air Resistance Force depends on the speed and the surface area of the object. Examples of Air Resistance Force are a person who is skydiving slows down because of the parachute, riding a bicycle, walking in a storm, etc.
  • Tension Force: Tension is a type of pulling force that is transmitted through a string, cable, etc. It acts along the string and exerts equal pressure at both ends. For example, drawing a bucket of water from a well, playing tug of war, weighing using a spring balance, etc.
  • Spring Force: Spring Force is exerted by a spring and it comes into play when a spring is stretched or compressed. Some examples that involve Spring Force are trampoline, shock absorbers in vehicles, spring balance, etc.

Action-at-a-Distance Force

Action-at-a-Distance Force is exerted without the objects being in contact. The various types of Action-at-a-Distance Force are as follows:

  • Gravitational Force: Gravitational Force is a universal force. It is a type of attractive force that explains the tendency of objects to fall towards the Earth. Gravitational Force is responsible for attracting any two objects with mass. Examples of the Gravitational Force are objects falling back on the Earth when thrown in the air, the working of our solar system is the result of the Sun’s gravitational force on other planets, etc.
  • Magnetic Force: Magnetic Force is the force of attraction or the force of repulsion that is exerted by the electrically charged particles due to their motion. Examples of Magnetic Force are motors, compasses, train tracks, etc.
  • Strong Nuclear Force: Strong Nuclear Force is responsible for the integrity of the atomic nucleus. It is exerted over very short distances.
  • Weak Nuclear Force: Weak Nuclear Force comes into play during atomic decay. Its range is even shorter than that of the Strong Nuclear Force.
  • Electrical Force: Electrical Force is the force of attraction or repulsion exerted between electrically charged particles. It is different from Magnetic Force as the charges are at rest in this case. Examples of Electrical Force are the charge in a bulb, electrical circuits, the attraction between two balloons when one of them is rubbed with hair, etc.