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Question

The potential energy of a particle varies with distance x from a fixed origin as U=(Ax)(x2+B), where Aand B are the dimensional constants, then find the dimensional formula for AB.


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Solution

Step1: Potential Energy and dimensional constants.

  1. Potential Energy: The energy possessed by an object due to its position.
  2. Dimensional Constants: A physical quantity with dimensions and a fixed value is referred to as a dimensional constant.

Step 2: Given parameters

  1. U=(Ax)(x2+B)

where, x is the distance from the fixed origin.

Step 3: Calculations

The potential energy of a particle varies with distance x from a fixed origin as,

U=(Ax)(x2+B)

From the principle of homogeneity,

x2=BB=L2

UnitofB=unitofx2=[L2]

U=A[x1/2](x2+B)

[ML2T-2]=A[L1/2][L2]A=[ML7/2T-2]AB=[ML7/2T-2][L2]AB=[ML11/2T-2]

Hence, the dimensional formula for AB is [ML11/2T-2].


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