Question

Which of the following is invariant under Galilean Transformation?
A. Velocity,
B. Linear Momentum,
C. Acceleration,
D. Length, E. Force. Choose the correct answer from the options given below:

• A. C, D, E Only
• B. A, B, C, D Only
• C. A, C, D, E Only
• D. A, B, C Only

Hint:

Under Galilean transformation, velocity changes but acceleration, length and force remain invariant.

Answer 1

The Correct Option is A

Concept:
Galilean transformation is used in classical mechanics to relate observations in two inertial frames moving with constant relative velocity.

Step 1: Check velocity.
Velocity changes from one inertial frame to another. \[ v'=v-u \] So, \[ A \text{ is not invariant} \]

Step 2: Check linear momentum.
Since velocity changes, linear momentum also changes. \[ p=mv \] So, \[ B \text{ is not invariant} \]

Step 3: Check acceleration.
Acceleration remains unchanged under Galilean transformation. \[ a'=a \] So, \[ C \text{ is invariant} \]

Step 4: Check length.
In classical mechanics, length is absolute. \[ D \text{ is invariant} \]

Step 5: Check force.
Since: \[ F=ma \] and acceleration is invariant, force is also invariant. \[ E \text{ is invariant} \] Therefore: \[ C,D,E \] \[ \therefore \text{Correct Answer is (A)} \]