Question

On a frictionless surface, a block of mass $M$ moving at speed $v$ collides elastically with another block of same mass $M$ which is initially at rest. After collision the first block moves at an angle $\theta$ to its initial direction and has a speed $\frac{v}{3}$. The second block's speed after the collision is

• A. $\frac{3}{\sqrt 2}v$
• B. $\frac{\sqrt3}{ 2}v$
• C. $\frac{2\sqrt 2}{3}v$
• D. $\frac{3}{4}v$

Answer 1

The Correct Option is C

The situation is shown in the figure.


Using energy conservation, $\frac{1}{2} m _{1} v _{1}^{2}+\frac{1}{2} m _{2} v _{2}^{2}=\frac{1}{2} m _{1} v _{1}^{\prime 2}+\frac{1}{2} m _{2} v _{2}^{\prime 2}$ here, $\frac{1}{2} Mv ^{2}+0=\frac{1}{2} M ( v / 3)^{2}+\frac{1}{2} Mv _{2}^{\prime 2}$
or $v _{2}^{\prime 2}=\frac{8}{9} v ^{2}$
or $v_{2}^{\prime}=\frac{2 \sqrt{2}}{3} v$

Answer 2

Ans. The conservation of Energy Formula denotes that energy can neither be created nor destroyed. Energy is the capacity to do any kind of work. On Earth, energy is available in multiple forms, varying from nuclear energy to electrical energy and so on. The law of conservation of energy is a very important concept of thermodynamics.

The Law of Conservation of Energy simply states that energy in all its form is never created or destroyed completely, it just transforms from one form to another.

• Every form of energy works on the principle of the law of energy conservation.
• In a system isolated from its surroundings (a closed system), the total energy remains conserved.
• So in an isolated system such as the universe, if there is a loss of energy in one part, there must be a gain of an equal amount of energy in some other part. 

The amount of energy in any system is determined by the conservation of energy equation. The conservation of energy formula can be represented as – 

U_T = U_i + W + Q

Where UT denotes the total energy of the system

• Ui represents the initial energy
• W is the work done on or by the system
• Q is the heat added or removed from the system

The change in the internal energy of the system can be determined by – 

ΔU = W+Q