NCERT Class 11 Physics Solutions: Chapter 5 – Laws of Motion Part 8

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Question 5.21:

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?

Answer:

Mass of the stone,

Radius of the circle,

Number of revolution per second,

Angular velocity,

The centripetal force for the stone is provided by the tension T, in the string, i.e.,

Maximum tension in the string,

Therefore, the maximum speed of the stone is 34.64 m/s.

Question 5.22:

If, in Exercise 5.21, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks:

(a) The stone moves radially outwards,

(b) The stoneflies off tangentially from the instant the string breaks,

(c) The stone flies off at an angle with the tangent whose magnitude depends on the speed of the particle.

Answer:

(b) The stoneflies off tangentially from the instant the string breaks :

When the string breaks, the stone will move in the direction of the velocity at that instant. According to the first law of motion, the direction of velocity vector is tangential to the path of the stone at that instant. Hence, the stone will fly off tangentially from the instant the string breaks.

Question 5.23:

Explain why

(a) A horse cannot pull a cart and run in empty space,

(b) Passengers are thrown forward from their seats when a speeding bus stops suddenly,

(c) It is easier to pull a lawn mower than to push it,

(d) A cricketer moves his hands backwards while holding a catch.

Answer:

(a) A horse cannot pull a cart and run in empty space:

In order to pull a cart, a horse pushes the ground backward with some force. The ground in turn exerts an equal and opposite reaction force upon the feet of the horse. This reaction force causes the horse to move forward. An empty space is devoid of any such reaction force. Therefore, a horse cannot pull a cart and run in empty space.

(b) Passengers are thrown forward from their seats when a speeding bus stops suddenly:

When a speeding bus stops suddenly, the lower portion of a passenger’s body, which is in contact with the seat, suddenly comes to rest. However, the upper portion tends to remain in motion (as per the first law of motion). As a result, the passenger’s upper body is thrown forward in the direction in which the bus was moving.

(c) It is easier to pull a lawn mower than to push it:

While pulling a lawn mower, a force at an angle is applied on it, as shown in the following figure:

Figure shown the While pulling a lawn mower, a force at an a …

Figur 5.23 (A)

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The vertical component of this applied force acts upward. This reduces the effective weight of the mower.

On the other hand, while pushing a lawn mower, a force at an angle θ is applied on it, as shown in the following figure.

On the other hand, while pushing a lawn mower, a force at an …

Figur 5.23 (B)

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In this case, the vertical component of the applied force acts in the direction of the weight of the mower. This increases the effective weight of the mower.

Since the effective weight of the lawn mower is lesser in the first case, pulling the lawn mower is easier than pushing it.

(d) A cricketer moves his hands backwards while holding a catch:

According to Newton’s second law of motion, we have the equation of motion:

Where,

F = Stopping force experienced by the cricketer as he catches the ball

m = Mass of the ball

= Time of impact of the ball with the hand

It can be inferred from equation (i) that the impact force is inversely proportional to the impact time, i.e.,

Equation (ii) shows that the force experienced by the cricketer decreases if the time of impact increases and vice versa.

While taking a catch, a cricketer moves his hand backward so as to increase the time of impact (). This is turn results in the decrease in the stopping force, thereby preventing the hands of the cricketer from getting hurt.