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If linear density of a rod of length 3m ...

If linear density of a rod of length 3m varies as `lamda=2+x`, then the position of the centre of mass of the rod is `P/7m`. Find the value of P.

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To find the value of \( P \) given that the linear density of a rod of length 3 m varies as \( \lambda = 2 + x \), we will calculate the center of mass of the rod using the definition of center of mass for a continuous distribution. ### Step 1: Define the linear density and mass element The linear density \( \lambda \) is given by: \[ \lambda(x) = 2 + x \] The mass element \( dm \) can be expressed as: ...
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