Physics Chapter on Significant Figures and Motion

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Questions and Answers

How many significant figures are in the number 0.00238?

5 (correct)

What is the dimensional formula for force?

M^1L^2T^3

M^1LT^-1

M^1L^2T^-2

M^1L^2T^-3 (correct)

What does the slope of a velocity-time graph represent?

Jerk

Displacement

Speed

Acceleration (correct)

In uniform motion, which statement about the velocity-time graph is true?

It is a straight line parallel to the time axis. Signup and view all the answers

For the number 82.380, how many significant figures are there?

5 Signup and view all the answers

Which of the following pairs correctly matches power with its dimensional formula?

M^1L^2T^-2 Signup and view all the answers

Identify the dimensional formula for work.

M^1L^2T^-2 Signup and view all the answers

Which of these statements about velocity is false during uniform motion?

Velocity varies over time. Signup and view all the answers

Which of the following is NOT one of the kinematic equations for an object under free fall?

v = 0.5(v0 + v)t Signup and view all the answers

What does Newton’s third law of motion state?

For every action, there is an equal and opposite reaction. Signup and view all the answers

Which of the following best describes the work-energy theorem for constant force?

Work done is equal to the change in kinetic energy. Signup and view all the answers

Which expression represents the total energy of an object orbiting around the Earth?

-rac{G M m}{r} Signup and view all the answers

The period of revolution of a satellite close to the surface of the Earth is primarily determined by which factor?

The gravitational acceleration at the surface of the Earth Signup and view all the answers

Which statement about centripetal acceleration is correct?

It is given by the formula $a_c = \frac{v^2}{r}$. Signup and view all the answers

What is the main factor affecting the optimum speed of a racecar on a banked track?

The angle of the banking Signup and view all the answers

What is the correct description of the moment of inertia of an object?

It’s a measure of the object's resistance to angular acceleration. Signup and view all the answers

When the torque acting on a system is zero, which quantity remains constant?

angular momentum Signup and view all the answers

If A, B, and C are vectors such that A × B = C, which statements are correct?

C is perpendicular to A + B Signup and view all the answers

The gravitational force between two bodies does not depend on which of the following?

sum of their masses Signup and view all the answers

Which statement about the value of acceleration due to gravity on Earth's surface is correct?

is maximum at the poles Signup and view all the answers

What is the formula for the orbital velocity of a satellite near the Earth's surface?

$2gR_E$ Signup and view all the answers

In the context of physics, the momentum of an object is directed towards which of the following?

the direction of its velocity Signup and view all the answers

The product of the component of the force in the direction of displacement and the magnitude of this displacement is known as what?

work done Signup and view all the answers

Which of the following statements about significant zeros is correct?

Trailing zeros in a decimal number are significant Signup and view all the answers

Which of the following pairs correctly match the physical quantity with its units?

(i) – (c), (ii) – (a), (iii) – (b) Signup and view all the answers

For an object moving with uniform acceleration, stopping distance is directly proportional to which of the following?

Square of initial velocity Signup and view all the answers

Identify the incorrect statement regarding an object moving with uniform velocity.

Instantaneous velocity is zero. Signup and view all the answers

If the velocity-time graph of an object is parallel to the time axis, what can be said about its acceleration?

Zero Signup and view all the answers

The magnitude of the vector A = Ax î + Ay ĵ + Az k̂ is represented by which of the following expressions?

√(Ax² + Ay² + Az²) Signup and view all the answers

Which statement is true regarding the path of a projectile?

It is a parabola. Signup and view all the answers

A body is said to be in equilibrium if which of the following conditions is met?

The resultant force is zero Signup and view all the answers

Where does the center of mass of three particles of equal masses lie?

At the centroid of the triangle formed by the particles Signup and view all the answers

What is the minimum speed required for an object to reach infinity called?

Escape velocity Signup and view all the answers

What unit is used to measure potential energy?

Joule Signup and view all the answers

What is instantaneous acceleration?

Rate of change of velocity at a specific moment Signup and view all the answers

Which expression defines the maximum velocity for a vehicle on a banked road?

$v_{max} = rac{r imes g imes an( heta)}{1}$ Signup and view all the answers

What is the impulse applied on a 500g cricket ball moving at 36 km/h and reflected back with the same speed?

10 kg·m/s Signup and view all the answers

What factors does centripetal acceleration depend on?

Speed and radius of the circular path Signup and view all the answers

How is work done by a variable force expressed mathematically?

W = ∫F·dx Signup and view all the answers

Study Notes

Significant Figures

Significant figures are digits that contribute to the precision of a number.
Leading zeros in a number with a decimal point are not significant.
Trailing zeros in a number with a decimal point are significant.

Dimensional Formulae

The dimensional formulae for physical quantities are as follows:
- Force: MLT⁻²
- Work: ML²T⁻²
- Power: ML²T⁻³

Kinematic Equations of Motion

The kinematic equations of motion for an object under free fall are:
- v = u + gt
- s = ut + ½gt²
- v² = u² + 2gs
- where: v = final velocity, u = initial velocity, g = acceleration due to gravity, t = time, and s = displacement.

Horizontal Range of a Projectile

The horizontal range of a projectile is the horizontal distance traveled by the projectile before it hits the ground.
The horizontal range is given by:
- R = (u² sin 2θ) / g
- where: u = initial velocity, θ = angle of projection, and g = acceleration due to gravity.

Newton’s Third Law of Motion

Newton’s third law of motion states that for every action, there is an equal and opposite reaction.
This means that when two objects interact, they exert forces on each other that are equal in magnitude and opposite in direction.
Example: When you push a wall, the wall pushes back on you with an equal and opposite force.

Work-Energy Theorem

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
This means that if you do work on an object, you are giving it energy.
The work-energy theorem can be expressed mathematically as:
- W = ∆KE
- where W is work done and ∆KE is the change in kinetic energy.

Linear Motion vs. Rotational Motion

Linear motion is the motion of an object along a straight line.
Rotational motion is the motion of an object around a fixed axis.
Some key differences include:
- Linear motion is characterized by displacement, velocity, and acceleration, while rotational motion is characterized by angular displacement, angular velocity, and angular acceleration.
- Linear momentum is conserved in linear motion, while angular momentum is conserved in rotational motion.

Total Energy of an Orbiting Satellite

The total energy of an orbiting satellite around the Earth is the sum of its kinetic energy and potential energy.
This total energy is constant and is given by:
- E = -GMm / (2r)
- where: G = gravitational constant, M = mass of the Earth, m = mass of the satellite, and r = orbital radius.

Period of Revolution of a Satellite

The period of revolution of a satellite very close to the surface of the Earth is given by:
- T = 2π√(RE/g)
- where: RE = radius of the Earth and g = acceleration due to gravity.

Velocity-Time Graph

A velocity-time graph is a graph that plots the velocity of an object as a function of time.
The slope of a velocity-time graph represents the acceleration of the object.
The area under a velocity-time graph represents the displacement of the object.

Centripetal Acceleration

Centripetal acceleration is the acceleration that is required to keep an object moving in a circular path.
It is always directed towards the center of the circle.
The magnitude of centripetal acceleration is given by:
- ac = v²/r
- where: v = velocity, and r = radius of the circular path.

Laws of Kinetic Friction

Friction is a force that opposes motion between two surfaces in contact.
Kinetic friction is the friction that occurs when two surfaces are sliding past each other.
Laws of kinetic friction state:
- The kinetic friction force is proportional to the normal force acting between the two surfaces.
- The kinetic friction force is independent of the area of contact between the surfaces.
- The kinetic friction force is independent of the relative speed of the surfaces.

Methods of Reducing Friction

Friction can be reduced by:
- Using lubricants: a substance applied between two surfaces that reduces friction by creating a thin layer of separation.
- Making surfaces smoother: smoother surfaces have less friction.
- Using ball bearings or roller bearings: reduces friction by rolling instead of sliding.
- Using air or fluid bearings: creates a thin layer of air or fluid between the surfaces that reduces friction.

Conservation of Mechanical Energy

The law of conservation of mechanical energy states that the total mechanical energy of a system remains constant if no external forces act on the system.
This means that the sum of the kinetic energy and potential energy of an object remains constant as long as no work is done by external forces.
This can be applied to a freely falling body by examining the potential and kinetic energy at different points during the fall.

Angular Momentum

Angular momentum is a measure of the amount of rotational inertia of a body.
It is a vector quantity and its direction is perpendicular to the plane of rotation.
The magnitude of angular momentum is given by:
- L = Iω
- where: I = moment of inertia, and ω = angular velocity.

Time Rate of Change of Angular Momentum

The time rate of change of angular momentum is equal to the net torque acting on the body.
This can be expressed mathematically as:
- dL/dt = τ

Escape Velocity

Escape velocity is the minimum velocity that an object needs to escape the gravitational pull of a planet or star.
This means that if an object is launched with escape velocity from the Earth’s surface, it will never fall back to Earth.
The escape velocity of an object from the Earth is derived from the equation:
- ve = √(2GM/R)
- where: G = gravitational constant, M = mass of the Earth, and R = radius of the Earth.

Magnitude and Direction of Resultant Vector

The magnitude of the resultant of two vectors A and B is given by:
- |R| = √(A² + B² + 2ABcosθ)
- Where: θ is the angle between A and B.
The direction of the resultant vector can be determined using the law of cosines.

Newton's Second Law of Motion

Newton's second law of motion states that the rate of change of momentum of a body is directly proportional to the force applied to it, and the change occurs in the direction of the applied force.
This means that the larger the force that is applied to an object, the larger its acceleration will be.
If we derive this into an equation we find that the force (F) is equal to the mass (m) of the object times its acceleration (a)
- F = ma

Instantaneous Power

Instantaneous power is the rate at which work is done at a particular instant in time.
The instantaneous power is given by:
- P = dW/dt
- where: P = power, W = work done, and t = time.

Commercial Unit of Electrical Power

The commercial unit of electrical power is the kilowatt-hour (kWh).
One kilowatt-hour is equal to the amount of energy used by a 1000 watt appliance for one hour.

Force, Work, and Power

The SI units of force, work, and power are:
- Force: Newton (N)
- Work: Joule (J)
- Power: Watt (W)
The relationships between them in terms of dimensions are:
- Force = MLT⁻²
- Work = ML²T⁻²
- Power = ML²T⁻³
The relationships between them in terms of units are:
- 1 J = 1 Nm
- 1 W = 1 J/s = 1 Nm/s

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Description

This quiz covers essential concepts in physics, such as significant figures, dimensional formulae, kinematic equations of motion, and projectile motion. Test your understanding of these fundamental topics to enhance your grasp of the subject. Perfect for students studying introductory physics.