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    A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m3 in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump?

    Given,

    Volume of the tank, V = 30 m3 

    Time of operation, t = 15 min

                                  = 15 × 60

                                  = 900 s 

    Height of the tank, h = 40 m 

    Efficiency of the pump, η = 30 % 

    Density of water, ρ = 103 kg/m3 

    Mass of water, m = ρV = 30 × 103 kg 

    Output power can be obtained as, 

    P0 = = 

        = 30 × 103 × 9.8 ×  

        =  13.067 × 10    3 W 

    For input power Pi,, efficiency η, is given by the relation, 
     
    η ==  30% 

    Pi =  

       = 0.436 × 105 W 

       =  43.6 kW, is the electric power consumed by the pump. 
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    Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V. If the collision is elastic, which of the following figure is a possible result after collision? 
    The total momentum before and after a collision in each case is constant.

    For an elastic collision,

    Total kinetic energy of a system remains conserved before and after the collision. 

    For mass of each ball bearing m, we can write, 

    Total kinetic energy of the system before collision, 

    = mV2 +(2m) × 02
    =mV2

    Case (i)

    Total kinetic energy of the system after collision, 

    =  m × 0 + (2m) ()2
    = mV2
    Hence, the kinetic energy of the system is not conserved in case (i).

    Case (ii)

    Total kinetic energy of the system after collision, 

    =x(2m) × 0 + mV2 
    =  mV2
    Hence, the kinetic energy of the system is conserved in case (ii). 


    Case (iii)

    Total kinetic energy of the system after collision, 

    = ()(3m)()2
    = ()mV2 

    Hence, the kinetic energy of the system is not conserved in case (iii). 

    Hence, Case II is the only possibility.
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    A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the trolley's floor at the rate of 0.05 kg m/s. What is the speed of the trolley after the entire sand bag is empty?
    Sand leaks from the trolley with the same velocity which the trolley has initially.
    Therefore, there is no change in momentum of sand and hence, the trolley.

    Therefore, after the entire bag is emptied, the velocity of the trooley remains the same, i.e., 27 km/hr.
    303 Views
    Answer
    The bob A of a pendulum released from 30° to the vertical hits another bob B of the same mass at rest on a table as shown. How high does the bob A rise after the collision? Neglect the size of the bobs and assume the collision to be elastic.
    The collision of bobs is elastic and masses of both the bobs are equal. Bob B is at rest, therefore, after collision of bob A with bob B, bob A comes to rest. Therefore, the bob A will not rise after the collision. 
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    Answer

    The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?

    Let m be the mass of bob and l be the length of the string. If potent

    Let m be the mass of bob and l be the length of the string. If potential energy of bob is taken zero at B, then potential energy of bob at A will be mgl. When bob reaches the point B, 5% of the potential energy is dissipated against air resistance, and rest of 95% is converted in kinetic energy.
    ∴                 1 half mv squared equals 0.95 mgl
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                               equals square root of 2 cross times 0.95 cross times 9.8 cross times 1.5 end root
                                equals 5.28 space straight m divided by straight s   
     
                                
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