what is the dimensional formula for (i) variable force (ii) movement of force (iii) linear density (iv)angular momentum
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1)Force = Mass x Acceleration
Acceleration = Change in Velocity/Time Taken
Acceleration = M0L1T-2
Substituting this in Force formula we get
Force = Mass x Acceleration
Force = M x M0L1T-2
So Dimensional Formula of Force= M1L1T-2
3)Linear Mass Density is defined as measure of mass per unit of length.
Mathematically,
Linear Mass Density = Mass / Length.
Dimensional Formula of Mass = M1L0T0.
Dimensional Formula of Length = M0L1T0.
Putting these values in above equation we get,
Dimensional Formula of Linear Mass Density = M1L-1T0.
4)Angular Momentum is a product of Moment of Inertia and Angular Velocity. Its formula is
Angular Momentum = Moment of Inertia X Angular Velocity
Dimensional Formula of Moment of Inertia= M1L2T0
Dimensional Formula of Angular velocity = M0L0T-1
Putting these values in above equation we get
So Dimensional Formula of Angular Momentum = M1L2T-1