## FSc Notes: Physics XI: Chapter 03 Motion and Force Exercise Short Questions:

**Question 3.1 What is the difference between uniform and variable velocity? From the explanation of variable velocity, define acceleration. Give SI units of velocity and acceleration.**

Answer 3.1

Answer 3.1

**Uniform Velocity:**The velocity of a body is said to be uniform if its direction and magnitude does not change with time. e.g. i) velocity of earth ii) velocity of satellites.

**Variable Velocity:**The velocity of a body is said to be variable if its direction or magnitude or both changes with time. A motion with variable velocity is called accelerated motion. In this case velocity may be increasing or decreasing. For e.g. motion of a car on road.

**Acceleration:**Rate of change of velocity is known as acceleration. When velocity is increasing acceleration is positive and when velocity is decreasing acceleration is negative.Units: The SI units of velocity is m/s and that of acceleration is m/s-2

**Question 3.2 An object is thrown vertically upward. Discuss the sign of acceleration due to gravity, relative to velocity, while the object is in air.**

Answer 3.2When an object is thrown upward its velocity is +ve and its acceleration due to gravity is –ve, as the object is moving against the direction of gravitational force. But at maximum height its velocity becomes zero and then it starts moving downward. Now its acceleration and velocity is +ve.

Answer 3.2

**Question 3.3 Can the velocity of an object reverse the direction when acceleration is constant? If so, give an example.**

Answer 3.3

Answer 3.3

**Yes**, velocity of an object can reverse direction when initially acceleration and velocity are opposite in direction. For e.g. when a body is thrown vertically upward its velocity goes on decreasing due to gravity, becomes zero at maximum height, and then the direction of the body is reversed.

**Question 3.4 Specify the correct statements:**

- An object can have a constant velocity even its speed is changing.
- An object can have a constant speed even its velocity is changing.
- An object can have a zero velocity even its acceleration is not zero.
- An object subjected to a constant acceleration can reverse its velocity.

**Answer 3.4**All statement are true expect: 1).

2) Circular motion.

3) When body is thrown upward, at maximum height.

4) Vertical motion.

**Question 3.5 A man standing on the top of a tower throws a ball straight up with initial velocity vi and at the same time throws a second ball straight downward with the same speed. Which ball will have larger speed when it strikes the ground? Ignore air friction.**

Answer 3.5Both the balls will have same speed when striking the ground. The ball thrown upward will pass from the same path with the same velocity while moving down and gains the same velocity as that of the ball thrown vertically downward, until it reaches the surface of the ground.Answer 3.5

**Question 3.6 Explain the circumstances in which the velocity v and the acceleration a of a car are:**- Parallel
- Anti-Parallel
- Perpendicular to one another
- v is zero but a is not zero
- a is zero but v is not zero.

**Answer 3.6**Circumstances in velocity v and acceleration a of a car are given below:

- When v and a are parallel the velocity of the car is increasing.
- When v and a are anti-parallel the velocity of the car is decreasing.
- When v and a are perpendicular, the car is moving in a circular path. Here velocity is along the tangent and acceleration is along the radius.
- v is zero when car comes to rest but acceleration is –ve but not zero or when there is a hurdle in front of the car it cannot move in the passage of car.
- When car move on a straight road with uniform speed (neglecting friction).

**Question 3.7 Motion with constant velocity is a special case of motion with constant acceleration, Is this statement true? Discuss.**

Answer 3.7Yes, motion with constant velocity is a special case of motion with constant acceleration. In this case the acceleration of the object is zero and velocity is uniform.

Answer 3.7

**Question 3.8 Find the change in momentum for an object subjected to a given force for a given time and state law of motion in terms of momentum.**

**Answer 3.8**Consider a body mass m moving with an initial velocity vi. Suppose an external force F acts upon it time t after which velocity becomes vf the acceleration a produced by the force is given by:

**a= vf – vi /t**

by second law on

**Newton a=F/m**

comparing two equations

**F /m = vf – vi /t or F x t= mvf – mvi**

where mvf is the final momentum and mvi is the initial momentum.

**F = (mvf – mvi )/t**

“

**Time rate of change of momentum of a body equals the applied force**”

**Question 3.9 Define impulse and show that how it is related to linear momentum?**

Answer 3.9Impulse is defined as the product of force and time i.e.

Answer 3.9

**Impulse = Force x Time**

**I=F x t= mvf - mvi**

I = pf - pi= p change in momentum

I= p

I = pf - pi= p change in momentum

I= p

**Question 3.10 State the law of conservation of linear momentum, pointing out the importance of isolated system. Explain, why under certain conditions, the law is useful even through the system is not completely isolated?**

Answer 3.10

Answer 3.10

**Law of conservation of linear momentum**: Total linear momentum of an isolated system remains constant. An isolated system is a system of bodies free from external force. This law holds good only for an isolated system. But under certain circumstances where external force is very small as compared to mutually interacting forces, the law can be applied to good approximation.

**Question 3.11 Explain the difference between elastic and inelastic collisions. Explain how would a bouncing ball behave in each case? Give plausible reasons for the fact that K.E is not conserved in most cases?**

Answer 3.11

Answer 3.11

A collision in which K.E remains constant after and before collision is called

**elastic collision**.

In a collision where K.E does not remains constant is called

**inelastic collision**.

Ideally the bouncing ball will rebound to some height in case of an elastic collision, but if it rebounds to nearly to the initial height, the collision is considered elastic one. In case of inelastic collision the ball will rebound to a small height as compared to dropping point.

**Question 3.12 Explain what is meant by projectile motion. Derive expressions for**

- the time of flight
- the range of projectile.

**Show that the range of projectile is maximum when projectile is thrown at an angle of 45 degree with the horizontal.**

Answer 3.12 Projectile Motion:

Answer 3.12 Projectile Motion:

**It is a two dimensional motion under constant acceleration due to gravity**

####
**1) The time of flight:**

**The time taken by the body to cover the distances from the place of its projection to the place where it hits the ground at the same level is called the time of flight.**This can be obtained by taking S=h=0, because the body goes up and comes back to the same level, thus covering no vertical distance. If the body is projecting with velocity v making angle with a horizontal, then its vertical components will be visinθ

**We have S = 0 ; vi = vi sinθ ; a = -g**

Using S = vi t + ½ a t2

⇒ 0 = vi sinθ t – ½ g t2

or t = 2 vi sinθ/g

t= 2vi sin/g

Using S = vi t + ½ a t2

⇒ 0 = vi sinθ t – ½ g t2

or t = 2 vi sinθ/g

t= 2vi sin/g

where

**t is the time of flight of the projectile**when it is projected from the ground.

####
**2) Range of the Projectile: **

**Maximum distance which a projectile covers in the horizontal direction is called the range of the projectile.**To determine the range R of the projectile, we multiply the horizontal components of the velocity of projection with the time taken by the body after leaving the point of projection thus. We have

**S = R , vx = vi cosθ, t = 2vi sinθ**

**Using S = v t g**

⇒ R = (vi cosθ x 2 vi sinθ)/g = (vi2 2 sinθ cosθ)/g

or R = (v sin 2θ)/g

for maximum range, sin 2θ should have maximum value ( i.e.) = 1

sin 2θ = 1 ⇒ 2θ = 90 ⇒ θ = 45

⇒ R = (vi cosθ x 2 vi sinθ)/g = (vi2 2 sinθ cosθ)/g

or R = (v sin 2θ)/g

for maximum range, sin 2θ should have maximum value ( i.e.) = 1

sin 2θ = 1 ⇒ 2θ = 90 ⇒ θ = 45

**Question 3.13 At what point or points in its path does a projectile have its minimum speed, its maximum speed?**

Answer 3.13A projectile has its minimum speed at the maximum height where vertical component of the velocity becomes zero. A projectile has its maximum speed at its minimum height if air friction is neglected.

Answer 3.13

**Question 3.14 Each of the following questions is followed by four answers, one of what correct answer.**

Identify that answer.

Identify that answer.

**1)What is meant by a ballistic trajectory?**

- The paths followed by an un-powered and unguided projectile.
- The paths followed by the powered and unguided projectile.
- The paths followed by an un-powered but guided projectile.
- The paths followed by an powered and guided projectile.

2)What happens when a system of two bodies undergoes an elastic collision?

2)What happens when a system of two bodies undergoes an elastic collision?

- The momentum of the system changes.
- The momentum of the system does not change.
- The bodies come to rest after collision.
- The energy conservation law is violated.

**i) The statement (a) is correct as ballistic trajectory follows an un-powered and unguided projectile.**

Answer 3.14

Answer 3.14

ii) The statement (b) is correct as momentum of the system does not change.

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