When a particle is thrown obliquely near the earth’s surface, it moves along a curved path under constant acceleration that is directed towards the center of the earth (we assume that the particle remains close to the surface of the earth). The path of such a particle is called a projectile and the motion is called projectile motion. Air resistance to the motion of the body is to be assumed absent in projectile motion.

In a Projectile Motion, there are two simultaneous independent rectilinear motions:

1. Along the x-axis: uniform velocity, responsible for the horizontal (forward) motion of the particle.
2. Along y-axis: uniform acceleration, responsible for the vertical (downwards) motion of the particle.

Water equivalent is defined as the amount of water that can replaces any substance gaining the same variation in temperature, when provided with the same amount of energy as that of substance. It is written as W.

Artificial satellite is a man-made device orbiting around the earth, moon or another planet transmitting to earth scientific information or used for communication.

These satellite revolve around the planets and prvided all the information about planet through satellite imagery.

Two types of artificial satellites :

1) Weather satellite : Help to predict weather.    ex. TIROS, COSMOS

2) Communication satellite : Allow telephone and data conversations to be relayed through satellite . ex. Telstar, Intelsat.

Work is said to be done when a force applied to an object moves that object.

We can calculate work by multiplying the force by the movement of the object.

W = F × d

The SI unit of work is the joule (J)

Steradian is a unit of measurement for the solid angles.

 Steradian is the angle subtended, at the center of a sphere, by a surface whose magnitude of area is equal to square of the radius of the sphere.

The solid angle of a sphere at it's centre is 4π steradians. 

For train A:
Initial velocity, u = 72 km/h = 20 m/s
Time, t = 50 s
Acceleration, aI = 0 (Since it is moving with a uniform velocity)
From second equation of motion, distance (sI)covered by train A can be obtained as:
s = ut + (1/2)at2
= 20× 50 + 0 = 1000 m
For train B:
Initial velocity, u = 72 km/h = 20 m/s
Acceleration, a = 1 m/s²
Time, t = 50 s
From second equation of motion, distance (sII) covered by train A can be obtained as:
sII = ut + (1/2)at2
= 20 X 50 + (1/2)  1  (50)2 = 2250 m
Hence, the original distance between the driver of train A and the guard of train B is 2250 - 1000 = 1250m.

The magnetic flux is given by

ϕ=LI

The dimensional formula of self inductance, [L]=[BA]/[I]​. . . . . .(1)

Force, f=qvB

[M¹L¹T⁻²]=[TA].[L¹T⁻¹].[B]

[B]=[M¹T⁻²A⁻¹]

[BA]=[M¹L²T⁻²A⁻¹]

From equation (1), we get

[ϕ]=[M¹L²T⁻²A⁻²]

Consider the linear motion of a body with an initial velocity u. Let the body accelerate uniformly and acquire a final velocity v after time t. The velocity–time graph is a straight line AB as shown below.

At t = 0, initial velocity = u = OA 

At t = t, final velocity = v = OC

The distance S travelled in time t = area of the trapezium OABD

s = (1/2) x (OA + DB) × OD

s = (1/2) x (u + v) × t  

Since v = u + at,

s = (1/2) x (u + u + at) × t

s = ut + (1/2) at²

Angular momentum is defined as:

The property of any rotating object given by moment of inertia times angular velocity.

It is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object. It is a vector quantity, which implies that here along with magnitude, the direction is also considered.

You may also want to check out these topics given below!

For elastic collision we can say

also here momentum is conserved

add above two equations

now initial kinetic energy

kinetic energy of 2nd block of mass 9m after collision

percentage of kinetic energy transferred is given by

so 36% of energy is transferred to stationary block in this collision

The coefficient of restitution (COR) is the ratio of the final to initial relative velocity between two objects after they collide.

It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision. A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic.

The speed of the helicopter is 100mile/h with respect to air.

Give v₁ a chance to be the speed of the helicopter 

What's more, v₂ be the speed of the breeze which has greatness b 

v₁ = 100 cos 60o i + 100 sin 60o j 

= 50i + 50√3j 

What's more, from the other idea 

  v₂ = an i 

the resultant is given by 

v₁ = v₁+v₂ 

=(50+a)i + 50√3j 

As given in the inquiry , the helicopter lands 45* east of north because of the breeze, at that point x part will be equivalent to y segment 

50+a = 50√3 

  a = 50(√3-1) 

 a = 36.6 miles/hr 

Cheers!!

Regards,

Vikas (B. Tech. 4^th year
Thapar University)

Simple Pendulum

A simple pendulum is defined as an object that has a small mass (pendulum bob), which is suspended from a wire or string having negligible mass.     

• Whenthe pendulum bob is displaced it oscillates on a plane about the vertical line through the support.
• Simple pendulum can be set into oscillatory motion by pulling it to one side of equilibrium position and then releasing it.

In the above image one end of a bob of mass m is attached to a string of length L and another to a rigid support executing simple harmonic motion.                            

Let us assume that T>0^∘C 
Heat lost by water= heat gained by ice to melt+ heat gained by water formed from ice
⇒300×1×(50−T)=150×80+150×1×(T−0) 
⇒T=6.7^∘C
⇒T=6.7^∘C
Hence our assumption that T>0^∘C  

There are three modes of heat transfer.

1. Conduction: Heat conduction is a process in which heat is transferred from the hotter part to the colder part in a body without involving any actual movement of the molecules of the body. Heat transfer takes place from one molecule to another molecule as a result of the vibratory motion of the molecules. Heat transfer through the process of conduction occurs in substances which are in direct contact with each other. It generally takes place in solids.
2. Convection: In this process, heat is transferred in the liquid and gases from a region of higher temperature to a region of lower temperature. Convection heat transfer occurs partly due to the actual movement of molecules or due to the mass transfer. For example. Heating of milk in a pan.
3. Radiation:  It is the process in which heat is transferred from one body to another body without involving the molecules of the medium. Radiation heat transfer does not depend on the medium. For example: In a microwave, the substances are heated directly without any heating medium.