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Just as precise measurements are necessary in science, it is equally important to be  able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity) :

(b) the mass of an elephant


Consider a ship of known base area floating in the sea. 


Let space it apostrophe straight s space depth space in space sea space equals space straight d subscript 1 space

Volume space of space water space displaced space by space ship space is comma space straight V subscript straight b equals Ad subscript 1

Now comma space move space an space elephant space on space the space ship. space

Let space the space dpeth space of space the space ship space be space now space straight d subscript 2 space

Vol. space of space water space displaced space by space the space ship
with space elephant space on space board comma space straight V subscript be space equals space Ad subscript 2 space

Vol. space of space water space displaced space by space elephant space equals space Ad subscript 2 space minus Ad subscript 1 space

Density space of space water space equals space straight D space

Mass space of space elephant space equals space AD space left parenthesis straight d subscript 2 space minus space straight d subscript 1 right parenthesis
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Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):
(c) the wind speed during a storm


Wind speed during a storm can be measured by an anemometer. As the wind blows, it rotates. The rotation made by the anemometer in one second gives the value of wind speed.
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Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):
(d) the number of strands of hair on your head


Area of the head surface carrying hair = A

Radius of hair strand can be measured using a screw gauge. 

Let radius of the hair strand be 'r'. 


Area space of space 1 space hair space equals space πr squared space

No. space of space strands space of space hair space equals space fraction numerator Total space surface space area over denominator Area space of space one space hair space end fraction space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator straight A over denominator space πr squared space end fraction
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It is claimed that two cesium clocks, if allowed to run for 100 years, free from any disturbance, may differ by only about 0.02 s. What does this imply for the accuracy of the standard cesium clock in measuring a time-interval of 1 s ?


When the time interval of 1 sec is measured, the accuracy in measurement is given by, 

 

Therefore, accuracy is 1 part in 1011

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Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity) :
(a) the total mass of rain-bearing clouds over India during the Monsoon.


straight A space Metrologist space records space about space 215 space cm space of space rainfall space in space India

space straight i. straight e. comma space the space height space of space water space column comma space straight h space equals space 215 space cm space equals space 2.15 space straight m

Ares space of space country comma space straight A space equals space 3.3 space cross times space 10 to the power of 12 space straight m squared

So comma space

Volume space of space rain space water comma space straight V space equals space straight A cross times space straight h space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 7.09 space cross times space 10 to the power of 12 space end exponent straight m cubed space

Density space of space water comma space straight rho space equals space 1 space cross times space 10 to the power of 3 space end exponent kg space straight m to the power of – 3 end exponent

Therefore comma space

Mass space of space rain space water equals straight rho space cross times space straight V space equals space 7.09 space cross times space 10 to the power of 15 space end exponent kg space

Hence comma space total space mass space of space rain space bearing
space clouds space over space India space equals space space 7.09 space cross times space 10 to the power of 15 space end exponent kg space
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