Explanation:

The given statements relate different physical quantities using mathematical equations. Let's analyze each statement separately.

Statement P: Force = acceleration due to gravity x mass

This statement relates force, mass and acceleration due to gravity. Force is a vector quantity which describes the interaction between two objects. Mass is a scalar quantity which describes the amount of matter in an object. Acceleration due to gravity is a vector quantity which describes the acceleration experienced by an object due to the gravitational force of the earth.

The dimension of force is given by [MLT^-2] (mass x length x time^-2). The dimension of acceleration due to gravity is given by [LT^-2] (length x time^-2). The dimension of mass is given by [M] (mass). Let's check if the dimensions of the left-hand side and right-hand side of the equation match.

Dimension of the left-hand side of the equation = dimension of force = [MLT^-2]
Dimension of the right-hand side of the equation = dimension of acceleration due to gravity x mass = [MLT^-2]

Hence, the dimensions on both sides of the equation match. Therefore, statement P is correct.

Statement Q: Electric charge = current x time

This statement relates electric charge, current and time. Electric charge is a scalar quantity which describes the property of matter that causes it to experience a force in an electromagnetic field. Current is a scalar quantity which describes the flow of electric charge. Time is a scalar quantity which describes the duration of an event.

The dimension of electric charge is given by [AT] (electric current x time). The dimension of current is given by [A] (electric current). The dimension of time is given by [T] (time). Let's check if the dimensions of the left-hand side and right-hand side of the equation match.

Dimension of the left-hand side of the equation = dimension of electric charge = [AT]
Dimension of the right-hand side of the equation = dimension of current x time = [AT]

Hence, the dimensions on both sides of the equation match. Therefore, statement Q is correct.

Statement R: Magnetic flux = Electric voltage x time

This statement relates magnetic flux, electric voltage and time. Magnetic flux is a scalar quantity which describes the amount of magnetic field passing through a given area. Electric voltage is a scalar quantity which describes the energy required to move an electric charge from one point to another. Time is a scalar quantity which describes the duration of an event.

The dimension of magnetic flux is given by [ML^2T^-2A^-1] (mass x length^2 x time^-2 x electric current^-1). The dimension of electric voltage is given by [ML^2T^-3A^-1] (mass x length^2 x time^-3 x electric current^-1). The dimension of time is given by [T] (time). Let's check if the dimensions of the left-hand side and right-hand side of the equation match.

Dimension of the left-hand side of the equation = dimension of magnetic flux = [ML^2T^-2A^-1]
Dimension of the right-hand side of the equation = dimension of electric voltage x time = [ML^2T^-3A^-1 x T] = [ML^2T^-2A^-1]

Hence, the dimensions on