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The amplitude of a simple pendulum,  oscillating in air with a small spherical bob,   decreases from 10 cm to 8 cm in 40 seconds.Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will  reduce  from  10  cm  to  5  cm  in  carbondioxide will be close to\left ( ln\: 5 = 1.601,ln\: 2= 0.693 \right )    

 

  • Option 1)

    231 s

  • Option 2)

    208 s

  • Option 3)

    161 s

  • Option 4)

    142 s

 

Answers (1)

best_answer

As we discussed in

As we know that

x\:=\:x_{o}e^{\frac{-bt}{2m}}

From question

8\:=\:10e^{\frac{40b}{2m}}------(i)

Similarly 5\:=\:10e^{\frac{-bt}{2m}}--------- (ii)

Solving equations (i) and (ii) we get

t\:\cong 142 sec


Option 1)

231 s

This option is incorrect.

Option 2)

208 s

This option is incorrect.

Option 3)

161 s

This option is incorrect.

Option 4)

142 s

This option is correct.

Posted by

Aadil

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