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Q.

Two vertical walls are separated by a distance of 2 metres. Wall ' $A$ ' is smooth while wall $B$ is rough with a coefficient of friction $μ = 0.5$ A uniform rod is probed between them. The length of the longest rod that can be probed between the walls is equal to

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a

$2 metres$

b

$2 \sqrt{2} m e t r e s$

c

$\sqrt{2} m e t r e s$

d

$\frac{\sqrt{17}}{2} m e t r e s$

answer is D.

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Detailed Solution

$μ N = m g$

Question Image

$& N_{1} = N_{2}$

Take the torque about the com

$N_{1} \frac{1}{2} \sin θ + N_{2} \frac{l}{2} \sin θ = μ N_{2} \frac{l}{2} \cos θ N_{1} \frac{1}{2} \sin θ \times 2 = μ N_{2} \times \frac{l}{2} \cos θ \tan θ = \frac{μ}{2}; \sqrt{\sec^{2} θ - 1} = \frac{1}{2} \sec θ = \sqrt{1 + \frac{l^{2}}{4}}; \frac{l}{2} = \sqrt{1 + \frac{0.25}{4}}; L = \sqrt{\frac{17}{2}} m t$

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