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A small sphere falls from rest in a viscous liquid. Due to friction, heat is produced. Find the relation between the rate of production of heat and the radius of the sphere at terminal velocity.A. `r^4`B. `r^3`C. `r^5`D. `r^2` |
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Answer» Correct Answer - C Rate of heat produced `=` power loss against vicous force `implies(dQ)/(dt)=F_vxxv_T` where the terminal velocity `v_T=(2r^2)/(9eta)(rho-sigma)g` and viscous force `F_v=6pietarv_T` Hence `(dQ)/(dt)=7pietarv_Txxv_T` or `v_Talphar^2` `implies(dQ)/(dt)proprv_T^2` but `v_Tpropr^2` Hence `(dQ)/(dt)propr^5` |
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