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It is a common observation that rain clouds can be at about a kilometre altitude above the ground.

(a) If a rain drop falls from such a height freely under gravity, what will be its speed? Also calculate in km/h. (g = 10m/s2)

(b) A typical rain drop is about 4mm diameter. Momentum is mass x speed in magnitude. Estimate its momentum when it hits ground.

(c) Estimate the time required to flatten the drop.

(d) Rate of change of momentum is force. Estimate how much force such a drop would exert on you.

(e) Estimate the order of magnitude force on umbrella. Typical lateral separation between two rain drops is 5 cm. (Assume that umbrella is circular and has a diameter of 1m and cloth is not pierced through !!)

0 29 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

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    Answered by

    Payal Gupta | Contributor-Level 10

    3 months ago

    This is a long answer type question as classified in NCERT Exemplar

    (a) velocity attained by a falling rain drop will be = 2 g h = 2 × 10 × 1000

    = 100 2 m s - 1 = 510 k m h

    (b) diameter of the rain drop = 2r=4mm

    Radius = 2mm= 2 × 10 - 3 m

    Mass of rain drop = V × ρ = 4 3 π r 3 ρ = 4 3 × 22 7 × 2 × 10 - 3 3 × 10 3 = 3.4 × 10 - 5 k g

    Momentum of rain drop= mv= 3.4 × 10 5 × 100 2 = 5 × 10 - 3 k g m / s

    (c) time ,t = d/v= 4 × 10 - 3 100 2 = 0.028 × 10 - 3 s

    (d) force exerted, F = change in momentum /time=

    (e) area = π R 2 = π × 1 2 2 = 11 14 = 0.8 m 2

    number of drops striking the the umbrella with separation of 5 × 10 - 2

    so net force = 0.8 ( 5 × 10 - 2 ) 2 × 168 = 53760 N

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