Question

Three blocks A, B and C of equal mass m are placed one over the other on a smooth horizontal ground as shown in figure. Coefficient of friction between any two blocks of A, B and C is ½. The maximum value of mass of block D so that the blocks A, B and C move without slipping over each other is –

• A. 6 m
• B. 5 m
• C. 3 m
• D. 4 m

Answer 1

Answer: (C)

3 m

Answer 2

Blocks A and C both move due to friction. But less friction is available to A as compared to C because normal reaction between A and B is less. Maximum friction between A and B can be:

f_max = µ m_Ag = $\left( \frac { 1 } { 2 } \right)$ mg

\ Maximum acceleration of A can be:

a_max = $\frac { \mathrm { f } _ { \max } } { \mathrm { m } }$ = $\frac { \mathrm { g } } { 2 }$

further a_max = $\frac { m _ { D } g } { 3 \mathrm {~m} + \mathrm { m } _ { \mathrm { D } } }$

or $\frac { \mathrm { g } } { 2 }$ = $\frac { m _ { D } g } { 3 \mathrm {~m} + \mathrm { m } _ { \mathrm { D } } }$ or m_D = 3m