Advertisements
Advertisements
प्रश्न
A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to ______.
विकल्प
`t^(1/2)`
t
`t^(3/2)`
`t^2`
Advertisements
उत्तर
A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to `bbunderline(t^(3/2))`.
Explanation:
Power P = Fν is constant.
⇒ `"P" = "m" "a" "ν " = "m""dν"/"dt" . "ν " (∵"a" = "dν"/"dt")`
⇒ `"ν ""dν"/"dt" = "P"/"m" `
⇒ `"ν ""d" "ν" = "P"/"m""d" "t"`
On integration, `"ν"^2/2 = "Pt"/"m" + "c"_1`
Let t = 0 at ν = 0 then c1 = 0
∴ `"ν"^2 = (2"P")/"m" "t"` or`"ds"/"dt" = sqrt((2"P")/"M") "t"` (∵) (`"ν" = "ds"/"dt"`)
∴ s = `sqrt((2"P")/"m") ∫ "t"^(1/2) "d" "t"`
s = `sqrt((2"P")/"m") . ("t"^(3/2))/(3/2) + "c"^2`
Let when t = 0 then s = 0 then c2 = 0
∴ `"s" = 2/3 sqrt((2"P")/"m") "t"^(3/2) => "s" ∝ "t"^(3/2)`
APPEARS IN
संबंधित प्रश्न
The blades of a windmill sweep out a circle of area A.
- If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time t?
- What is the kinetic energy of the air?
- Assume that the windmill converts 25% of the wind’s energy into electrical energy, and that A = 30 m2, v = 36 km/h and the density of air is 1.2 kg m–3. What is the electrical power produced?
A family uses 8 kW of power.
- Direct solar energy is incident on the horizontal surface at an average rate of 200 W per square meter. If 20% of this energy can be converted to useful electrical energy, how large an area is needed to supply 8 kW?
- Compare this area to that of the roof of a typical house.
The S.I. unit of power is ..........
1 H.P. = .........
Two coolies A and B do some work in time 1 minute and 2 minute respectively. The power spent is
The expression of power P is
1 H.P. is equal to
A pump raises water by spending 4×105J of energy in 10s. Find the power of the pump.
An electric pump has 2 kW power. How much water will the pump lift every minute to a height of 10 m?
If a 1200 W electric iron is used daily for 30 minutes, how much total electricity is consumed in the month of April?
A ball with a velocity of 5 ms−1 impinges at an angle of 60˚ with the vertical on a smooth horizontal plane. If the coefficient of restitution is 0.5, find the velocity and direction after the impact.
An engine develops 20 kW power. How much time will it take to lift a mass of 200 kg to a height of 50 m? (g = 10 m/s2)
An engine pumps up 200 kg of water through a height of 20 m in 10 seconds. If the efficiency of the engine is 80%. Calculate the power of the engine.
The average work done by a human heart while it beats once is 0.5 J. Calculate the power used by heart if it beats 72 times in a minute.
Calculate the power spent by a crane while lifting a load of mass 2000 kg, at velocity of 1.5 ms-1. (g = 10 ms-2)
Name the quantity which is measured in kWh.
Name the quantity which is measured in Wh.
Name the quantity which is measured in eV.
