Question

A ladder $AB$ is supported by a smooth vertical wall and rough horizontal floor as shown. A boy starts moving from $A$ to $B$ slowly. The ladder remains at rest, then pick up the correct statement(s):

• A. Magnitude of normal reaction by wall on ladder at point $B$ will increase.
• B. Magnitude of normal reaction by wall on ladder at point $B$ will decrease.
• C. Magnitude of normal reaction by floor on ladder at point $A$ will remain unchanged.
• D. Magnitude of frictional force by the floor on ladder at point $A$ will increase.

Answer 1

Answer: (A), (C), (D)

The correct options are
A Magnitude of normal reaction by wall on ladder at point $B$ will increase.
C Magnitude of normal reaction by floor on ladder at point $A$ will remain unchanged.
D Magnitude of frictional force by the floor on ladder at point $A$ will increase.



Let $m$ and $M$ be mass of man and ladder. From FBD normal reaction at $A$ is $N_1=(m+M)g$ which remains constant. Net torque on man + ladder is zero about $B$. If $x$ decreases then torque of $mg$ about $B$ will decrease.
Hence $f$ must increase.