If in a hypothetical system if the angular momentum and mass are dimensionless. Then which of the following is true.
The power varies as .
The explanation for correct option
Step 1: Given
Mass is dimensionless:
Angular momentum is dimensionless:
Step 2: Formula Used
Force is given by the formula , where is mass and is acceleration.
Power is given by the formula , where is force and is velocity.
Work done or energy is given by the formula , where is force and is displacement.
Linear momentum is given by the formula , where is mass and is velocity.
Step 3: Solution
From and , it can be written that
Option A
We know that the dimension of velocity is . Calculate the linear momentum using the formula ,
Thus, option A is correct. The linear momentum varies as .
Option B
We know that the dimension of force is and displacement is . Calculate the energy using the formula ,
Thus, option B is correct. The energy varies as .
Option C
We know that the dimension of force is and velocity is . Calculate the power using the formula ,
Thus, option C is correct. The power varies as .
The explanation for incorrect option
Option D
We know that the dimension of acceleration is . Calculate the power using the formula ,
Thus, option D is incorrect. The force does not vary as .
Hence, options A, B, and C are correct.