NCERT Class 11 Physics Solutions: Chapter 5 – Laws of Motion Part 12

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Question 5.33:

A monkey of mass climbs on a rope in shown in figure. which can stand a maximum tension of In which of the following cases will the rope break: the monkey

(a) Climbs up with an acceleration of

(b) Climbs down with an acceleration of

(c) Climbs up with a uniform speed of

(d) Falls down the rope nearly freely under gravity?

(Ignore the mass of the rope).

Case (a):

Mass of the monkey,

Acceleration due to gravity,

Maximum tension that the rope can bear,

Acceleration of the monkey,

Using Newton’s second law of motion, we can write the equation of motion as:

Since , the rope will break in this case.

Case (b):

Acceleration of the monkeydownword

Using Newton’s second law of motion, we can write the equation of motion as:

Since , the rope will not break in this case.

Case (c):

The monkey is climbing with a uniform speed of 5 m/s. Therefore, its acceleration is zero,

i.e., a = 0.

Using Newton’s second law of motion, we can write the equation of motion as:

Since , the rope will not break in this case.

Case (d):

When the monkey falls freely under gravity, its will acceleration become equal to the acceleration due to gravity, i.e.,

Using Newton’s second law of motion, we can write the equation of motion as:

Since , the rope will not break in this case.

Question 5.34:

Two bodies A and B of masses and in contact with each other rest on a table against a rigid wall shown in figure. The coefficient of friction between the bodies and the table is . A force of is applied horizontally to A. What are

The reaction of the partition

The action-reaction forces between A and B?

What happens when the wall is removed? Does the answer to change, when the bodies are in motion?

Ignore the difference between

The reaction of the partition:

Mass of body A,

Mass of body B,

Applied force,

Coefficient of friction,

The force of friction is given by the relation:

leftward

Net force acting on the partition

As per Newton’s third law of motion, the reaction force of the partition will be in the direction opposite to the net applied force.

Direction opposite to the net applied force.

Hence, the reaction of the partition will be , in the leftward direction.

The action-reaction forces between A and B:

Force of friction on mass A:

leftward

Net force exerted by mass A on mass B rightward

As per Newton’s third law of motion, an equal amount of reaction force will be exerted by mass B on mass A, i.e., acting leftward.

When the wall is removed, the two bodies will move in the direction of the applied force.

Net force acting on the moving system

The equation of motion for the system of acceleration a, can be written as:

Net force

Net force causing mass A to move:

Net force exerted by mass A on mass B

This force will act in the direction of motion. As per Newton’s third law of motion, an equal amount of force will be exerted by mass B on mass A, i.e., acting opposite to the direction of motion.