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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA non-uniform thin rod of length \( L \) has linear mass density given by \( \lambda(x) = k x^2 \), where \( x \) is measured from its left end and \( k \) is a constant. The position of its centre of mass from the left end is:
Correct answer · Option 4
\( \frac{3}{4}L \)
Explanation
\( X_{\text{cm}} = \frac{\int_0^L x (k x^2) dx}{\int_0^L k x^2 dx} = \frac{k \int_0^L x^3 dx}{k \int_0^L x^2 dx} = \frac{L^4/4}{L^3/3} = \frac{3}{4}L \).
