Figure shown a cylindrical tube of radius r and lengh l fitted with a cork. The friction coefficient between the cork and the tube is mu. The tube contains an ideal gas at temperature T, and atmospheric pressure P_(0) Thetube is slowly heated , the cork pipe out when temperature is boubled. What is normal force per unit length exerted by the periphery of tube? Assume uniform temperature throughout gas any instant.

Figure shown a cylindrical tube of radius r and lengh l fitted with a

1.	Figure shown a cylindrical tube of radius r and lengh l fitted with a cork. The friction coefficient between the cork and the tube is mu. The tube contains an ideal gas at temperature T, and atmospheric pressure P_(0) Thetube is slowly heated , the cork pipe out when temperature is boubled. What is normal force per unit length exerted by the periphery of tube? Assume uniform temperature throughout gas any instant.
Answer» <P> Solution :SINCE volume of the gas is constant, `(P_(i))/(T_i)=(P_f)/(T_(f)` `P_(f)=P_(i)((T_(F))/T_(i))=2P_(i)=2P_(0)` The Forces actihg on the CORK are shown in the FIGURE in equilibrium. `P_(0)xxA+muN=2P_(0)A` `N=(P_(0)A)/mu` `N` is the total normal force exerted by the tube on the cork, hence contact force per unil length is `(dN)/(dl)=(N)/(2pir)`=`(P_(0)A)/(2pimur)`