A body of mass m = 10 − 2   kg is moving in a medium and experiences a frictional force F =…

A body of mass m=10−2 kg is moving in a medium and experiences a frictional force F=−k v 2 . Its initial speed is v0=10 m s−1. After 10 s its kinetic energy is 18mv02, then value of k will be:-
  1. 10−1 kg m-1 s-1
  2. 10−3 kg m-1
  3. 10−3 kg s-1
  4. 10−4 kg m-1

Solution

After 10 sec, 12mv2=18mv02
⇒v=v02=5 m s-1
Acceleration,  a=− k v 2 m
⇒  dv dt =− k v 2 m
⇒ ∫105dvv2=−km ∫010dt
-15+110=-k10-2×10
k=10−4 kg m-1

Asked in: JEE Main 2017 (02 Apr)

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