InterviewSolution
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InterviewSolution
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It is common observation that rain clouds can be at about a kilometre altitude above the grond. (a) If a rain drop falls from such a height freely under gravity, what will be its speed ? Also calculate in km //h. (g=10 m//s^2) (b) A typical rain drop is about ` 4 mm` diameter. Vomentum is mass xxspeed in vagnitude . Estimate its momentum when it hits ground. (c ) Estimate the time required to flatten the drop. (d) Rete of change of momentum id force. Fstmate how much forece such a drop would exert you. (e) Estiate the order of magitude force of magnitude force on umbrella.Typical lateral separation between tao rain drops is ` 5 cm`. (Assume that umbrella is circular and has a diameter of `1 m` and cloth is not prierced through it) |
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Answer» Here, ` h= 1000 m, g=10 m//s^2` (a) Velcoity of rain drop after fallin height (h) si ` v = sqrt (2 gh) = sqrt (2 xx 10 xx 1000) = 100 sqrt 2 m//s = ( 100 sqer 2 xx 60 xx 60)/(1000) km// h = 36 0 sqrt 2~~ 510 km //h` (b) Diameter of drop, ` d = 2 =4 mm or r= 2 mm = 2 xxx 10^(-3)m` Mass of rain drop, ` m= 4/3/ pi r^3 roh = 4/3 xx (220/7 xx ( 2 xx 10^3)^3 xx 10^(-3)^3 xx 10^3 ~~ 3.4 xx 10 ^(-5) kg` Mumentum of rain drop when it hits the ground, ` P = mu = ( 3.4 xx 10 ^(-5) xx 100 sqrt 2 ~~ 4.7 xx 10^(-3) kg m//s` (c ) Time required to flatten the frop is ` Delta t = d/v = (4 xx 10^(-3))/(100 sqrt 2) = 0/028 xx 10^(-3) = 28 xx 10^(-6) s` (d) Force, ` F= (change in momentum )/(time) = ( P-0)/(Delta t) = ( 4. 7 xx 10^(-3))/(28 xx 10^(-6)) ~~ 16 8 N` (e) Given , rakies of umbrella, ` R = 1//2 m` Area of umbrella ` =pi R^2 = 922) /7 9 1/2 )^2 = (22)/(28) = (11)/(14) ~~ 0.8 m^@` with average separaion of ` 5 cm (= 5 xx 10^(-2) m), number of drops those will hit nubrella simultanceously ` = (0.8)/((5 xx 10^(-2))^2` Net force on umbrella`= 320 xx 168 = 53760 N ~~ 54000 N`. |
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