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In the figure shown, there is a rod AB of mass m and length L is lying on a rough incline surface of inclination $θ = 37 °$ with horizontal. Co-efficient of friction $μ = 1 .0$ . Select correct observation/s

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Repeated expansion and contraction can cause the rod to slide up the incline

The rod expands on heating and there is a point on the rod which does not move. The distance of this point from B is 0.875L

Repeated expansion and contraction can cause the rod to slide down the incline

The rod contracts, on cooling and there is a point which does not move. The distance of this point is found as 0.125 L from end B

answer is A, B, C.

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Detailed Solution

$f_{1} - f_{2} = mgsinθ \Rightarrow μ \frac{m}{L} gxcosθ - μ \frac{m}{L} (L - x) gcosθ = mgsinθ$

$x = \frac{L}{2} [1 + \frac{tanθ}{μ}] = 0 .875 L$

On cooling friction changes its direction
Hence $f_{2} - f_{1} = mgsinθ$
$y = 0 .125 L$

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