d potential energy of a particle varies wid distance 'x' from a fixed origin as;-U=A root /x square + B - Physics - Units And Measurements

Question

d potential energy of a particle varies wid distance 'x' from a
fixed origin as;-U=A root /x square + B , WHERE A and B are
dimensional constants then WHAT WILL be dimensional formula for
AB?

Vijay Yadav · Accepted Answer

Dear Student,

U=Axx2+B  
 1Where U=Potential energyx=distanceDimensional formula of potential energy, U=M1L2T-2Dimensional formula of distance, x=M0L1T0From equation 1, we can writex2=-BB=-M0L1T02B=-M0L2T0Dimensional formula of B=M0L2T0We can write equation 1 as,U=Axx2U=Ax32A=Ux32A=M1L2T-2×M0L1T032A=M1L2T-2×M0L32T0A=M1+0L2+32T-2+0A=M1L72T-2A
B=M1L72T-2M0L2T0A B=M1L72+2T-2A B=M1L112T-2

d potential energy of a particle varies wid distance 'x' from a fixed origin as;-U=A root /x square + B , WHERE A and B are dimensional constants then WHAT WILL be dimensional formula for AB?