# NCERT Class 11 Physics Solutions: Chapter 5 – Laws of Motion Part 15 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 5.39:

A man stands in contact against the inner wall of a hollow cylindrical drum of radius rotating about its vertical axis with The coefficient of friction between the wall and his clothing is What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

Mass of the man,

Coefficient of friction,

Frequency of rotation,

The necessary centripetal force required for the rotation of the man is provided by the normal force

When the floor revolves, the man sticks to the wall of the drum. Hence, the weight of the man (mg) acting downward is balanced by the frictional force acting upward.

Hence, the man will not fall until:

The minimum angular speed is given as:

Question 5.40:

A thin circular loop of radius rotates about its vertical diameter with an angular frequency . Show that a small bead on the wire loop remains at its lowermost point for . What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ?

Neglect friction.

Let the radius vector joining the bead with the centre make an angle , with the vertical downward direction.

Normal reaction

The respective vertical and horizontal equations of forces can be written as:

we have:

Substituting equation in equation, we get:

Substituting equation in equation, we get:

Since the bead will remain at its lowermost point for , i.e.. , for

On equating equations and we get:

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