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A thin rod of length 'L' is lying along ...

A thin rod of length 'L' is lying along the `x`-axis with its ends at `x=0` and `x=L` its linear (mass/length) varies with `x` as `k((x)/(L))^n`, where n can be zero of any positive number. If to position `x_(CM)` of the centre of mass of the rod is plotted against 'n', which of the following graphs best apporximates the dependence of `x_(CM)` on n?

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
A
Linear density `rho ( = "mass"//"length") = k ((x)/(L))^(n)`
when `n = 0, rho =` constant. The c.m will be at the centre of the ord, i.e. at `x = L//2`.
As n increases to 1, 2, 3,….,linear density goes on increasing. The c.m shifts beyond `x = L//2`, towards `x = L`. For sufficiently large values of n, the c.m tends to be at the other end `x = L` of the rod.
Graph (a) in Fig. is the best appoximation of dependence of `x_(cm)` on n.
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