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Class 10 Class 12

A body of mass m = 10–2 kg is moving in a medium and experiences a frictional force F = –kv2. Its initial speed is v0 = 10 ms–1. If, after 10 s, its energy is 1/8 mv02,the value of k will be

  • 10-4 kg m-1

  • 10–1 kg m–1 s–1

  • 10-3 kg m-1

  • 10-3 kg s-1


A.

10-4 kg m-1

1 half mv subscript straight f superscript 2 space equals space 1 over 8 mv subscript 0 superscript 2
straight v subscript straight f space equals space straight v subscript 0 over 2 space equals space 5 space straight m divided by straight s
left parenthesis 10 to the power of negative 2 end exponent right parenthesis space dv over dt space equals space minus space kv squared
integral subscript 10 superscript 5 space dv over straight v squared space equals negative 100 space straight k integral subscript 0 superscript 10 space dt
1 fifth space minus space 1 over 10 space equals space 100 space straight k space left parenthesis 10 right parenthesis
straight k space equals space 10 to the power of negative 4 end exponent
1 half mv subscript straight f superscript 2 space equals space 1 over 8 mv subscript 0 superscript 2
straight v subscript straight f space equals space straight v subscript 0 over 2 space equals space 5 space straight m divided by straight s
left parenthesis 10 to the power of negative 2 end exponent right parenthesis space dv over dt space equals space minus space kv squared
integral subscript 10 superscript 5 space dv over straight v squared space equals negative 100 space straight k integral subscript 0 superscript 10 space dt
1 fifth space minus space 1 over 10 space equals space 100 space straight k space left parenthesis 10 right parenthesis
straight k space equals space 10 to the power of negative 4 end exponent
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