Q. What is unit vector?
Ans. Such vector whose magnitude is one is called unit vector
unit vector = `\frac{\text {vector}}{\text {magnititude of vector}}`
Q. Define momentum.
Ans. The product of mass and velocity of the body is called momentum. It is a vector quantity.
Formula
`\text {Momentum} = \text{mass}\times\text{velocity}`
`P = m v`
S.I. unit of momentum is `\frac{Kg m}{s}`
Dimensional formula of momentum `[M^1L^1T^{-1}]`
Q. Define Force in Physics?
Ans. A push or a pull on an object is called force and it is equal to the product of mass and acceleration.
Force = mass `\times` acceleration
F = m a
S.I. unit of force is `\frac{Kg \times m}{s^2}`
Dimensional formula of force `[M^1L^1T^{-2}]`
Q. What is specific heat?
Units of specific heat are J/(kg K) or J/(kg °C)
`S = \frac{\Delta Q}{m \Delta T}`
Q. Define acceleration?
Ans. The rate of change of velocity of an object is called acceleration. Acceleration is a vector quantity because it has both magnitude and direction. It is denoted by a or f. The unit of acceleration is `\frac{m}{s^2}` and the dimensional formula is `[M^0L^1T^{-2}]`.
Acceleration = `\frac{\text{Change in velocity}}{\text{Time taken}}`
`a = \frac {dv}{dt}`
Q. Define velocity?
Ans. Rate of change in displacement with respect to time is known as velocity. Velocity is a vector quantity that has both magnitude and direction.
Formula
`\text{Velocity} = \frac{\text{Displacement}}{\text{Time}}`
`v = \frac {s}{t}`
Unit of velocity - m/s
Dimensions of velocity is `[M^0L^1T^{-1}]`
Q. Write 3 equations of motion.
Ans.
1. `v = u + at`
2. `S = ut + \frac{1}{2}at^2`
3. `v^2 = u^2 + 2as`
Where
v = final velocity
u = initial velocity
a = acceleration
t = time
S = displacement
Q. Define work done by a constant force.
Ans. The scalar product of the force acting on an object and the displacement caused by the force is called work. Work is a scalar quantity denoted by W.
`dW = \vec{ F}.\vec{ds}`
`W = \int \vec{ F}.\vec{ds}`
S.I. unit of work done is Joule (J).
Other units of work done are
(1) N`\times` m
(2) `\frac {Kg\times m}{s^2}`
Dimensions of work done are `[M^1L^2T^{-2}]`
Q. What is law of inertia?
Ans. Newton's first law is the law of inertia, according to this law, if an object is at rest, it remains at rest and if an object is in motion, it will remain in motion as long as there is no external force on that object.
Q. What is the second law of motion?
Ans. The rate of change of momentum of an object is equal to the force exerted on the object.
`\text{Force} = \frac{\text{Change in momentum}}{\text{Time taken}}`
`F = \frac{dp}{dt}`
`F = \frac{d(mv)}{dt}` `(\because p = mv)`
`F = m \frac{dv}{dt}`
`F = m a` `(\because a = \frac{dv}{dt})`
`\text{Force} = \text{mass}\times\text{acceleration}`
Ans. According to this law, for every action, there is an equal and opposite reaction.
`\vecF_2 = - \vecF_1`
Ans. Every liquid tries to minimize its surface area. This property of liquid is called surface tension. It is denoted by T.
`\text{Surface Tension} = \frac{\text{Force}}{\text{Length}}`
`T = \frac{F}{l}`
Where,
T = Surface Tension
F = Force
l = Length
Unit of Surface Tension is N/m and the Dimensions are `[M^1L^0T^{-2}]`
Ans. An adiabatic process is a thermodynamic process in which no heat transfer takes place.
Ans. Such physical quantities which have magnitude and units but no direction are called scalar quantities.
Examples of scalar quantity - mass, length, speed, time, work, density, etc.
Ans. Such physical quantities which have magnitude and unit, as well as direction, are called vector quantities.
Examples of vector quantity - displacement, velocity, acceleration, momentum, force etc.
Ans. Fundamental Quantities
Q. What is the speed of light?
Ans. The speed of light depends on the medium in which the light waves travel. The highest speed of light in a vacuum is 299,792,458 meters per second or `3 \times 10^8` m/s (approximately).
Ans. Such physical quantities that can be derived from fundamental quantities it means derived quantities can be found by division and multiplication.
Example - Speed is a derived quantity it can be derived by fundamental quantities length(distance) and time.
`\text{Speed} = \frac{\text{Length(distance)}}{\text{Time}}`
Ans. The velocity of any object A with respect to another object B is known as relative velocity.
`\Delta V = V_B - V_A`
Example: Two trains running in the same direction with velocities A and B than the relative velocity of train A with respect to train B is -
`\Delta V = V_B - V_A`
Ans. There are 4 fundamental forces of nature -
(1) Gravitational Force
(2) Electromagnetic force
(3) Strong nuclear force
(4) Weak nuclear force
Q. What is the acceleration due to gravity?
Ans. The acceleration gained by an object by an object is known as the acceleration due to gravity.
`\star` It is denoted by g.
`\star` It is a vector quantity.
`\star` Values of g in SI: 9.806 `m s^2`
`\star` Dimensional Formula: `[M^0L^1T^{-2}]`
Ans. The minimum velocity required to any object to escape from the gravitational field of that planet is escape velocity.
Ans.
Orbital Velocity
The minimum velocity a body must maintain to stay in orbit is orbital velocity.
Ans.
Universal Law of Gravitation
The force of attraction between two masses is directly proportional to the product of the mass of both bodies and inversely proportional to the distance between them.
Formula
`F = \frac{G m_1 m_2}{r^2}`
Where
F = force
G = Universal Gravitational Constant
`G = 6.67 \times 10^{- 11}\frac{N m^2}{kg^2}`
`m_1`= mass of object 1
`m_2` = mass of object 2
r = distance between centers of the masses
Ans. Torque is the measure of the force that can cause an object to rotate about an axis. It is denoted by `\tau`.
`\star` `\tau` is a vector quantity.
`\star` The SI unit for torque is the Newton`\times` metre or `{kg m^2}/s^{2}`.
`\star` Dimensional formula - `[M^1L^2T^{-2}]`
`\star` `\vec{\tau} = \vec r \times \vec F`
Ans.
Angular momentum
The product of the moment of inertia and the angular velocity of the rotating object.
`J = I \omega`
The vector product of linear momentum and distance is called angular momentum. It is denoted by J. It is a vector quantity.
`\vec J = \vec r \times \vec p`
`\star` It is denoted by J.
`\star` It is a vector quantity.
`\star` Dimensional Formula: `[M^1L^2T^{-1}]`
Q. Define angular acceleration.
Ans. The rate of change in angular velocity with respect to time.
`\alpha=\frac{\Delta \omega}{\Delta t}=\frac{\omega_{2}-\omega_{1}}{t_{2}-t_{1}}`
`\alpha` = angular acceleration
`\Delta \omega` = change in angular velocity
`\Delta t` = change in time
`\omega_{2}` = final angular velocity
`\omega_{1}` = initial angular velocity
`t_{2}` = final time
`t_{1}` = initial time
`\star` It is denoted by `\alpha`.
`\star` It is vector quantity.
`\star` Angular acceleration unit is radian/`s^2`
`\star` Dimensional Formula: `[M^0L^0T^{-2}]`
Ans. The time taken by an object for one complete oscillation is called the time period.
`\star` It is denoted by T.
`\star` It is a scalar quantity.
`\star` Unit of time period is second.
`\star` Dimensional Formula: `[M^0L^0T^1]`
Ans.
The number of vibrations or oscillations per unit time is called frequency.
(or)
Frequency is the number of occurrences of a repeating event per unit of time.
`\star` It is denoted by n or f.
`\star` It is a scalar quantity.
`\star` Unit of frequency is Hertz(Hz.) of `s^{-1}`.
`\star` Dimensional Formula: `[M^0L^0T^{-1}]`
Ans. The perpendicular force per unit area is called Pressure.
Formula of pressure
`\text{Pressure} = \frac{\text{Force}}{\text{Area}}`
`\star` It is denoted by P.
`\star` It is a scalar quantity.
`\star` Unit of pressure is `\frac{N}{m^2}`.
`\star` Dimensional Formula: `[M^1L^{-1}T^{-2}]`
Ans.
| Sr.No. | Distance | Displacement |
|---|---|---|
| 1. | It is length of travelled path. | It is shortest distance between initial and final point. |
| 2. | It is a scalar quantity. | It is a vector quantity. |
| 3. | Distance can never be zero. | Displacement can be positive and negative both. |
Ans. According to Newton's law of cooling, the rate of loss of heat of a body is directly proportional to the difference between the temperature of that body and the temperature of the medium around it (atmosphere). In other words, this law states that the value of 'heat transfer coefficient' remains constant.
`- \frac{d\theta}{dt} = K (\theta - \theta_0)`
`- (\frac{\theta_2 - \theta_1}{t_2 - t_1}) = K (\frac{\theta_1 + \theta_2}{2} - \theta_0)`
Where
`\theta_1 =`Temperature on time `t_1`
`\theta_2 =`Temperature on time `t_2`
`\theta_0 = `Temperature of atmosphere.
Law of Conservation of Momentum
Unless an external force is applied, the total momentum of the system remains constant.
`\frac{dp}{dt} = F`
When F = 0
`\frac{dp}{dt} = 0`
`P = Constant`
or
`P_1 = P_2`
`m_1 v_1 = m_2 v_2`
Ans.
Kepler's law of planetary motion
Kepler's first law of planetary motion
Each planet revolves around the Sun in an elliptical orbit. Elliptical orbit has two focus, the Sun is at one focus.
Kepler's second law of planetary motion
All the planets cross the same area in the same time interval, that is, the areal speed of all the planets remains the same.
Kepler's third law of planetary motion
The squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits.
Electrostatics Class 12 Chapter 1 Detailed Notes
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