Q.

In figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle θ with the horizontal floor. The coefficient of friction between the wall and the ladder is μ1 and that between the floor and the ladder isμ2. The normal reaction of the wall on the ladder is N1 and that of the floor is N2. If the ladder is about toslip, then

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a

μ1=0μ2≠0 and N2tan⁡θ=mg2

b

μ1≠0μ2=0 and N1tan⁡θ=mg2

c

μ1≠0μ2≠0 and N2=mg1+μ1μ2

d

μ1=0μ2≠0 and N1tan⁡θ=mg2

answer is C.

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Detailed Solution

If μ1=0,μ2≠0t1=0, balancing torques about AN1ℓsin⁡θ=mgcos⁡θ2; N1tan⁡θ=mg2 If μ1≠0,μ2≠0T2=0, equilibrium cannot be attained.  If μ1≠0,μ2≠0N1=t2=μ2N2;N2+t1=mgN2+μ1N1=mg; N2+μ1μ2N2=mg; N2=mg1+μ1μ2
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In figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle θ with the horizontal floor. The coefficient of friction between the wall and the ladder is μ1 and that between the floor and the ladder isμ2. The normal reaction of the wall on the ladder is N1 and that of the floor is N2. If the ladder is about toslip, then