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Yogita Ingle 6 years, 5 months ago
Minimum subscription refers to the minimum amount required by the company for its preliminary functions. It has been provided by the Companies Act, that the company must receive applications for a certain minimum number of shares before going ahead with the allotment of shares in order to prevent companies from commencing business with inadequate resources. This is called the ‘minimum subscription’. The limit of minimum subscription is 90% of the size of the issue.
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Yogita Ingle 6 years, 5 months ago
Bernoulli’s Principle
- For a streamline fluid flow, the sum of the pressure (P), the kinetic energy per unit volume (ρv2/2) and the potential energy per unit volume (ρgh) remain constant.
- Mathematically:- P+ ρv2/2 + ρgh = constant
- where P= pressure ,
- E./ Volume=1/2mv2/V = 1/2v2(m/V) = 1/2ρv2
- E./Volume = mgh/V = (m/V)gh = ρgh
Derive: Bernoulli’s equation
Assumptions:
- Fluid flow through a pipe of varying width.
- Pipe is located at changing heights.
- Fluid is incompressible.
- Flow is laminar.
- No energy is lost due to friction:applicable only to non-viscous fluids.
- Mathematically: -
- Consider the fluid initially lying between B and D. In an infinitesimal timeinterval Δt, this fluid would have moved.
- Suppose v1= speed at B and v2= speedat D, initial distance moved by fluid from to C=v1Δt.
- In the same interval Δtfluid distance moved by D to E = v2Δt.
- P1= Pressureat A1, P2=Pressure at A2.
- Work done on the fluid atleft end (BC) W1 = P1A1(v1Δt).
- Work done by the fluid at the other end (DE)W2 = P2A2(v2Δt)
- Net work done on the fluid is W1 – W2 = (P1A1v1Δt− P2A2v2Δt)
- By the Equation of continuity Av=constant.
- P1A1 v1Δt - P2A2v2Δt where A1v1Δt =P1ΔV and A2v2Δt = P2ΔV.
- Therefore Work done = (P1− P2) ΔVequation (a)
- Part of this work goes in changing Kinetic energy, ΔK = (½)m (v22 – v12) and part in gravitational potential energy,ΔU =mg (h2 − h1).
- The total change in energy ΔE= ΔK +ΔU = (½) m (v22 – v12) + mg (h2 − h1). (i)
- Density of the fluid ρ =m/V or m=ρV
- Therefore in small interval of time Δt, small change in mass Δm
- Δm=ρΔV (ii)
- Putting the value from equation (ii) to (i)
- ΔE = 1/2 ρΔV (v22 – v12) + ρgΔV (h2 − h1) equation(b)
- By using work-energy theorem: W = ΔE
- From (a) and (b)
- (P1-P2) ΔV =(1/2) ρΔV (v22 – v12) + ρgΔV (h2 − h1)
- P1-P2 = 1/2ρv22 - 1/2ρv12+ρgh2 -ρgh1(By cancelling ΔV from both the sides).
- After rearranging we get,P1 + (1/2) ρ v12 + ρg h1 = (1/2) ρ v22 + ρg h2
- P+(1/2) ρv2+ρg h = constant.
- This is the Bernoulli’s equation.
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Yogita Ingle 6 years, 5 months ago
PPC is concave to the origin because of increasing Marginal opportunity cost. This is because inorder to increase the production of one good by 1 unit more and more units of the other good have to be sacrificed since the resources are limited and are not equally efficient in the production of both the goods.
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Yogita Ingle 6 years, 5 months ago
Physical education is a course taught in school that focuses on developing physical fitness and the ability to perform and enjoy day-to-day physical activities with ease.Kids, as well as adults, benefit from regular exercise. Health benefits from regular exercise include: stronger muscles and bones, increased coordination and energy, and decreased risk of developing chronic diseases such as type 2 diabetes. For most kids, exercise means being physically active during play, recess, and physical education class, also known as P.E. Physical education contributes to each child’s total growth and development. Kids also develop skills necessary to participate in a wide range of activities, such as soccer, basketball, or swimming. Regular physical education classes prepare kids to be physically and mentally active, fit, and healthy into adulthood. An effective physical education program should include engaging lessons, trained P.E. teachers, adequate instructional periods, and student evaluation.
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