Work, Energy and Power
- How much water, a pump of 2 kW can raise in one minute to a height of 10 m, take g = 10 m/s2 ?
-
View Hint View Answer Discuss in Forum
P = W Here, P = 2kW = 2000 W. t
W = Mgh = M × 10 × 10 = 100 M and t = 60 s.
This gives, M = 1200 kg
Its volume = 1200 litre as 1 litre of water contains 1 kg of its mass.Correct Option: B
P = W Here, P = 2kW = 2000 W. t
W = Mgh = M × 10 × 10 = 100 M and t = 60 s.
This gives, M = 1200 kg
Its volume = 1200 litre as 1 litre of water contains 1 kg of its mass.
- 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 energy. How much power is generated by the turbine?( g = 10 m/s2)
-
View Hint View Answer Discuss in Forum
Given, h = 60m, g = 10 ms–2,
Rate of flow of water = 15 kg/s
∴ Power of the falling water = 15 kgs–1 × 10 ms–2 × 60 m = 900 watt. Loss in energy due to friction = 9000 × 10 = 900 watt 100
∴ Power generated by the turbine = ( 9000 – 900) watt
= 8100 watt = 8.1 kWCorrect Option: A
Given, h = 60m, g = 10 ms–2,
Rate of flow of water = 15 kg/s
∴ Power of the falling water = 15 kgs–1 × 10 ms–2 × 60 m = 900 watt. Loss in energy due to friction = 9000 × 10 = 900 watt 100
∴ Power generated by the turbine = ( 9000 – 900) watt
= 8100 watt = 8.1 kW
- A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest
-
View Hint View Answer Discuss in Forum
Power exerted by a force is given by P = F.v
When the body is just above the earth’s surface, its velocity is greatest. At this instant, gravitational force is also maximum. Hence, the power exerted by the gravitational force is greatest at the instant just before the body hits the earth.Correct Option: B
Power exerted by a force is given by P = F.v
When the body is just above the earth’s surface, its velocity is greatest. At this instant, gravitational force is also maximum. Hence, the power exerted by the gravitational force is greatest at the instant just before the body hits the earth.
- A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude Po. The instantaneous velocity of this car is proportional to :
-
View Hint View Answer Discuss in Forum
Constant power of car P0 = F.V = ma.v
P0 = m dv .v dt
P0 dt = mv dv
IntegratingP0 t = mv2 2
∵ P0 , m and 2 are constant
∴ v ∝ √tCorrect Option: B
Constant power of car P0 = F.V = ma.v
P0 = m dv .v dt
P0 dt = mv dv
IntegratingP0 t = mv2 2
∵ P0 , m and 2 are constant
∴ v ∝ √t
- One coolie takes 1 minute to raise a suitcase through a height of 2 m but the second coolie takes 30 s to raise the same suitcase to the same height. The powers of two coolies are in the ratio of
-
View Hint View Answer Discuss in Forum
∵ Power P = w t ⇒ P1 = t2 = 30 s = 30 s = 1 P2 t1 1 minute 60 s 2
(t1 = 1 minute; t2 = 30 second given)
Correct Option: A
∵ Power P = w t ⇒ P1 = t2 = 30 s = 30 s = 1 P2 t1 1 minute 60 s 2
(t1 = 1 minute; t2 = 30 second given)
