Question

Assertion: The concept of pseudo force is valid for both the inertial as well as non-inertial frame of reference.
Reason: A frame accelerated with respect to an inertial frame is non- non-inertial frame.
(A) Both assertion and reason are correct and reason is the correct explanation of assertion.
(B) Both assertion and reason are correct and reason is not the correct explanation for assertion.
(C) Assertion is correct but reason is incorrect.
(D) Assertion is incorrect but reason is correct.

Answer 1

Hint Force always acts when there is an acceleration produced in the body and for non-accelerating body or body moving with constant velocity, we deal with such motion in an inertial frame of reference.

Complete Step By Step Solution
1. Motion of an object is always determined by a well-defined system of coordinates. Hence, motion is relative. This well-defined frame of reference is known as frame of reference. Also, Frame of reference can be defined as a coordinate system (Cartesian coordinate system) relative to which the position and motion of a body may be described. This frame of reference is categorized into two types:
2. Inertial frame of reference – In which Newton laws’ are obeyed and holds good.
We know, from Newton’s second law of motion that;
\[\overrightarrow F = m\overrightarrow a \]
Where, \[\overrightarrow F \] = force applied on particle/ object,
\[\overrightarrow a \]= acceleration of particle
m = mass of particle
In an inertial frame of reference, the external force acting on a particle is zero always.
\[
   \Rightarrow \overrightarrow F = 0 \\
   \Rightarrow m\overrightarrow a = 0 \\
 \]
Now, \[m \ne 0\]
\[ \Rightarrow \overrightarrow a = 0\]
\[\therefore \]Inertial frames of references are also known as non- accelerating frames of references.
3. Non-inertial frame of reference- In which, Newton's law doesn't hold good. And non- inertial frames of references are called accelerated frames of references. Let’s take an example, a man sitting in a bus at rest, when brakes are applied, the body of man tends to move in forward direction, that means acceleration is produced or some movement is produced in body without applying any force on body while he was initially sitting in rest position. So, it was supposed that a pseudo force is producing acceleration in the body while there is no actual force working on the body.
Here, \[\overrightarrow a \] has some value.
Now, the assertion says that the concept of pseudo force is valid for both the inertial as well as non-inertial frame of reference. But there is no acceleration in a particle when it is in an inertial frame of reference and hence no force is acting on the particle/ object. But when the particle is considered to be non-Inertial frame of reference, \[\overrightarrow a \] has some value. And a pseudo force is acting on a body. Thus, the concept of pseudo force is valid only for non-inertial frames of reference.
Similarly, Reason says that a frame accelerated with respect to an inertial frame is non- non-inertial frame which is true. Since from the definition also we know that an accelerating frame of reference is a non-inertial frame of reference.

Thus we can conclude that, option (D) is correct, i.e. Assertion is incorrect but reason is correct.

Note whenever a frame of reference deals with acceleration, it is always a non-inertial frame of reference and for inertial frame of references, \[\overrightarrow a = 0\]and body either is at rest or is moving with a constant velocity and no pseudo force acts on the body.