Q38 of 48 Page 46

A raindrop of mass 1.00 g falling from a height of 1 km hits the ground with a speed of 50 m s–1. Calculate

(a) the loss of P.E. of the drop.


(b) the gain in K.E. of the drop.


(c) Is the gain in K.E. equal to loss of P.E.? If not why.


Take g = 10 m s-2


Mass m of drop = 1g = 0.001 kg


Change in height Δ h = 1 km = 1000 m


Final velocity = 50


∵ the drop starts from rest, initial velocity = 0


∴ initial K.E = 0 J


And final K.E =


a) Loss in P.E. =


b) Gain in K.E.


c) No, the gain in K.E. equal to loss of P.E. is not the same because of resistance like drag and viscous force against the drop.


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36

Consider a one-dimensional motion of a particle with total energy E. There are four regions A, B, C and D in which the relation between potential energy V, kinetic energy (K) and total energy E is as given below:

Region A: V > E


Region B: V < E


Region C: K > E


Region D: V > K


State with reason in each case whether a particle can be found in the given region or not.


 37

The bob A of a pendulum released from horizontal to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. 6.13. If the length of the pendulum is 1m, calculate

(a) the height to which bob A will rise after collision.


(b) the speed with which bob B starts moving. Neglect the size of the bobs and assume the collision to be elastic.



 39

Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (Fig. 6.14). One of the bobs is released after being displaced by 100 so that it collides elastically head-on with the other bob.

(a) Describe the motion of two bobs.


(b) Draw a graph showing variation in energy of either pendulum with time, for 0 ≤ t ≤ 2T, where T is the period of each pendulum.



 40

Suppose the average mass of raindrops is 3.0 × 10-5 kg and their average terminal velocity 9 m

s-1. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.