A uniform ladder of mass 10 kg leans against a smooth vertical wall making an angle 53° with it. The other end rests on a rough horizontal floor. Find the normal force and the frictional force that the floor exerts on the ladder

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30 N

65 N

50 N

120 N

answer is B.

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Detailed Solution

The ladder is in equilibrium
$∴ N_{1} = f and N_{2} = W$
Taking torque about ‘B’
$\begin{array}{l} N_{1} (AO) = W (CB) (or) \\ N_{1} (AB) \cos 53 = W (\frac{AB}{2}) \sin 53 \end{array}$
$\begin{array}{l} (or) N_{1} = \frac{2}{2} W and \\ N_{2} = W = 10 \times 9 .8 = 98 N \\ f = N_{1} = \frac{2}{3} W = 65 N \end{array}$

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