Question

A uniform rod of length ‘l’ and mass ‘M’ has been placed on rough horizontal surface as shown in figure. The rod is pulled by applying a horizontal force. Friction coefficient between surface and rod is ‘m’ given by :

m =

Heat generated as rod moves by a distance ‘L’ is-

• A. $\frac { \mu \mathrm { MgL } ^ { 2 } } { 2 }$
• B. mMg $L ^ { 2 }$
• C. $\frac { \mu \mathrm { MgL } ^ { 2 } } { 3 }$
• D. $\frac { \mu \mathrm { MgL } ^ { 2 } } { 6 }$

Answer 1

Answer: (A)

$\frac { \mu \mathrm { MgL } ^ { 2 } } { 2 }$

Answer 2

Heat generated = – (Work done by friction)

W_f = $\int _ { 0 } ^ { \mathrm { L } } \mu \left( \frac { \mathrm { L } - \mathrm { x } } { \mathrm { L } } \cdot \mathrm { M } \right) \mathrm { g }$ = – $\frac { \mu \mathrm { MgL } ^ { 2 } } { 2 }$