NCERT Class 11 Physics Solutions: Chapter 7 – System of Particles and Rotational Motion Part 8

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Question 7.22:

As shown in Figure, the two sides of a step ladder and are 1.6 m long and hinged at . A rope , is tied half way up. A weight is suspended from a point from along the ladder . Assuming the floor to be frictionless and neglecting the weight of the ladder, find the tension in the rope and forces exerted by the floor on the ladder. (Take ) ( Consider the equilibrium of each side of the ladder separately.)

As shown in Figure, the two sides of a step ladder BA and CA …

Figure Shown the All Condition of Question

Answer:

The given situation can be shown as:

In Figure,NB = Force exerted on the ladder by the floor poin …

Tension in the Rope Forces Exerted by the Floor on the Ladde …

Force exerted on the ladder by the floor point B

Force exerted on the ladder by the floor point C

Tension in the rope

Mass of the weight,

Draw a perpendicular from on the floor . This intersects at mid-point .

and are similar,

Hence, is the mid-point of

is the mid-point of .

Hence, we can write:

Using equations we get:

Hence, is the mid-point of

and is the mid-point of. Hence, will also be the midBpoint of and are similar

In

For translational equilibrium of the ladder, the upward force should be equal to the downward force.

For rotational equilibrium of the ladder, the net moment about is: