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 ______.
पर्याय
`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 S.I. unit of power is ..........
Two coolies A and B do some work in time 1 minute and 2 minute respectively. The power spent is
A pump raises water by spending 4×105J of energy in 10s. Find the power of the pump.
It takes 20 s for a girl A to climb up the stairs while girl B takes 15 s for the same job. Compare the work done .
It takes 20 s for a girl A to climb up the stairs while girl B takes 15 s for the same job. Compare the power spent by then.
Differentiate between watt and watt hour.
If a 1200 W electric iron is used daily for 30 minutes, how much total electricity is consumed in the month of April?
Choose one or more correct alternatives.
Power is a measure of the ______.
- The rapidity with which work is done.
- Amount of energy required to perform the work.
- The slowness with which work is performed.
- Length of time.
Arrive at an expression for power and velocity. Give some examples for the same.
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.
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? (g = 10m/s2)
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? (g = 10 m/s2)
A man is throwing bricks of mass 2 kg onto a floor from a height of 2 m. Bricks reach the floor at a speed `2sqrt(10)` m/s. Man throws 10 bricks in a minute. If the power of man is W watt then `3/10` W is equal to ______ W.
Sand is being dropped from a stationary dropper at a rate of 0.5 kgs-1 on a conveyor belt moving with a velocity of 5 ms-1. The power needed to keep belt moving with the same velocity will be ______.
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)
Unit of power used in mechanical engineering is ______.
Name the quantity which is measured in kW.
At any instant of time t, the displacement of any particle is given by 2t – 1 (SI unit) under the influence of force of 5N. The value of instantaneous power is (in SI unit):
