NCERT Class 11 Physics Solutions: Chapter 5 – Laws of Motion Part 7

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Question 5.18:

Two billiard balls each of mass 0.05 kg moving in opposite directions with speed collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?

Answer:

Mass of each ball

Initial velocity of each ball

Magnitude of the initial momentum of each ball,

After collision, the balls change their directions of motion without changing the magnitudes of their velocity.

Final momentum of each ball,

Impulse imparted to each ball = Change in the momentum of the system

The negative sign indicates that the impulses imparted to the balls are opposite in direction.

Question 5.19:

A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s–1, what is the recoil speed of the gun?

Answer:

Mass of the gun,

Mass of the shell,

Muzzle speed of the shell,

Recoil speed of the gun = V

Both the gun and the shell are at rest initially.

Initial momentum of the system = 0

Final momentum of the system = mv – MV

Here, the negative sign appears because the directions of the shell and the gun are opposite to each other.

According to the law of conservation of momentum:

Final momentum = Initial momentum

Question 5.20:

A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)

Answer:

The given situation can be represented as shown in the following figure:

figure shown the given situation.

Figure 5.20

Loading image

Where,

AO = Incident path of the ball

OB = Path followed by the ball after deflection

∠AOB = Angle between the incident and deflected paths of the ball = 45°

∠AOP = ∠BOP = 22.5° = θ

Initial and final velocities of the ball = v

Horizontal component of the initial velocity = along RO

Vertical component of the initial velocity = along PO

Horizontal component of the final velocity = along OS

Vertical component of the final velocity = along OP

The horizontal components of velocities suffer no change. The vertical components of velocities are in the opposite directions.

∴ Impulse imparted to the ball = Change in the linear momentum of the ball

Mass of the ball,

Velocity of the ball,

∴ Impulse