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Question

What is the dimension of 12at2?


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Solution

Step 1: Dimensional formula

  1. The dimensional formula of acceleration is given by M0L1T-2.
  2. The dimensional formula of Time Period is given by M0L0T1.

Here,

M is the mass, L is the length, and T is the temperature.

Step 2: The dimension of 12at2

12at2=12[M0L1T-2][M0L0T1][M0L0T1]=12×L1T2×T2=12[L1]

Therefore, 12at2has the dimension of length since the dimension of acceleration is LT2 and multiplying it by T2 leaves us with the dimension of lengthL.


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