## A doubt from Dimensional Analysis

What about the correctness about the relation,

s_{t}=u+0.5a(2t-1), both dimensionally or any other

Prakash Adhikari asked

**Answer**

The equation refers to the displacement in the **t ^{th} second** and hence it should have the dimensions of speed; since it is the

**displacement in one second**.

Under this consideration, the equation is dimensionally and otherwise correct.

## Thoughts on Higgs Boson

When it is not contested scientifically that change is a continuous phenomenon,how is that **Higgs boson**, if found,can be considered as the ultimate building block of matter.

Sure, it may prove a mathematically arrived conclusion… yet the contradiction remains.

An ever changing, at the same time, ever stable (because it is the ultimate one) is the contradiction.

One may find changing or divisible particle only…

(Posted by K.C. Muralidhar)

**Please post your thoughts and reactions as comments to this post**

## Electric Field at the centre of a half ring

A thin half-ring of radius R=20cm is uniformly charged with a total charge q=0.70nC.Find the magnitude of the electric field strength at the centre of this half-ring.

## Problem from Kinematics

the distance between Ahmadabad and vadodara is 100 km.two trains set off simultaneously from Ahmadabad towards vadodara each other.the speed of these trains are 45kmh-1 And 30kmh-1.when will they cross each other?

## A Few problems from Projectile Motion

1. If R and H are the horizontal range and maximum height attained by a projectile, than what is its speed of projection? please explain .

2. A particle projected from ground at angle 45 degrees with horizontal from distance ‘d1’ from the foot of a pole and just after touching the top of pole it falls on ground at a distance ‘d2’ from pole on other side, then what is the height of pole?please explain.

3. A particle projected from ground moves at angle 45 degrees with horizontal one second after projection and speed is minimum two seconds after the projection.What is the angle of projection of particle?(neglect the effect of air resistance) please explain.

4.A particle is moving on a circular path with constant speed v. It moves between two points A and B, which subtends an angle 60 degree at the centre of the circle. What are the magnitude of change in its velocity and change in magnitude of its velocity during motion from A to B respectively? please explain

Asked Shruti Suman Acharya

Answer

1.

## How to determine the diameter of a rod using thread an meter scale?

You are given a sufficiently long piece of thread, a meter stick and a thin round shape iron rod. Explain how would you measure the diameter of iron rod by using given thread and meter stick.

Yosef asked

Answer:

Wind the thread over the rod closely a number of times say 20 and mark the end point. Now unwind it and measure the length of the thread used to wind over the rod.

This length = n x 2πr, where n is the no. of windings and r is the radius of the rod.

Therefore, the diameter of the rod = 2r = The length of wire used for ‘n’ windings /nπ

## Why there is a 4(pi) in Coulomb’s law?

Why there is a 4π in Coulomb’s law?

Asked Rick Ghosh

Answer:

This is a consequence of geometry.

Please remember that Coulomb’s law is stated originally for **point charges ** at rest. By symmetry, a point charge should exert equal force on a test charge at all points equidistant from it, which constitute a spherical shell of surface area **4πr ^{2}**.

This consideration itself suggests the inverse square relation ship as well as the need for **4π.**

That was actually my explanation for it.

The term 4π was not there when Coulomb’s law was first stated in cgs system. The term 4π was introduced in SI on rationalization of units based on Maxwell’s equations of electromagnetism.

But I feel that my earlier explanation is simple and convincing.

Hope you got it.

Further discussions are welcome.