Sujit Prasad Kushwaha

                                                                  New Syllabus Course Title: Scientific Communication                                                                   Full Marks:50 Course No: SC 101                                                   ...

Conservation of Linear Momentum The total quantity of motion contained in a body is called linear momentum . It is denoted by $\vec{P}$ and defined as the product of mass and velocity of the body. For a body of mass $m$ and velocity $v$, its linear momentum $\vec{P}$ in vector form is given by: $$\vec{P} = m\vec{v}$$ In terms of magnitude only, $$P = mv$$ SI unit of linear momentum is $\text{kg m s}^{-1}$ or Ns, and dimensional formula is $[MLT^{-1}]$. Law of Conservation of Linear Momentum It states that, "the total linear momentum of a system of particles remains constant, provided that no external force acts on the system" . Proof: From Newton's second law of motion , $$F = \frac{dP}{dt}$$ In absence of force, $$\frac{dP}{dt} = 0 \;\Rightarrow\; P = \text{constant}$$ Proof (for a system of particles): Let us consider a system of $n$ particles of total mass $M$. Then, $$M = m_1 + m_2 + \cdots + m_n$$ So, $$P = P_1 + P_2 + \cdots + P_n$$ Differe...

Have you ever thought what are the most commonly used Mathematics Formulae? Yes, many of you have. Let me convert your imagination into reality. Here are some of the most commonly used mathematics formulas: 1. Quadratic Formula:  $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ where a, b, and c are coefficients of quadratic equation. 2. Pythagoras Theorem: $$a^2+b^2=c^2$$ where a, b, and c are the length of the sides of a right-angle triangle. 3. Distance Formula: $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$ where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinate of two points in a plane. 4. Area of a Circle: $$A=\pi{r^2}$$ where r is the radius of the circle. 5. Volume of a Sphere: $$V=\frac{4}{3}\pi{r^3}$$ where r is the radius of the sphere. 6. Volume of a Cylinder: $$V=\pi{r^2}h$$ where r is the radius and h is the height of the cylinder. 7. Area of a Triangle: $$A=\frac{1}{2}bh$$ where b is the base of the triangle and h is the height. 8. Slope-intercept formula: $$y=mx+c$$ where m is the slope o...

 1. Read the following passage and answer the questions given below briefly: [10] There is a considerable scientific disagreement about the medical hazards of the new pollutants; about the effects of DDT now found in human bodies, about the diseases due to smog, or about the long range effects of fallout. But the crucial point is that the disagreements exists, for they reveal that we have risked these hazards before we know what harm they might do. Unwittingly we have loaded the air with substances that interfere with the functioning of the blood. Because we wanted to build nuclear bombs and kill mosquitoes; we have burdened our bodies with strontium-90 and DDT, with consequences that no one can now predict. We are, in effect, conducting a high experiment ourselves. A generation hence-too late to help-public health statistics may reveal what hazards are associated with these pollutants. ('Science and Survival,' Barry commoner) a) What are the three pollutants with which man has...

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