Question

Two blocks of masses M₁ and M₂ are connected with a string passing over a pulley as shown in figure. The block M₁ lies on a horizontal surface . The coefficient of friction between the block M₁and the horizontal surface is m. The system accelerates. What additional mass m should be placed on the block M₁ so that the system does not accelerate?

• A. $\frac { \mathrm { M } _ { 2 } - \mathrm { M } _ { 1 } } { \mu }$
• B. $\frac { \mathrm { M } _ { 2 } } { \mu } - \mathrm { M } _ { 1 }$
• C. $M _ { 2 } - \frac { M _ { 1 } } { \mu }$
• D. (M₂ – M₁)m

Answer 1

Answer: (B)

$\frac { \mathrm { M } _ { 2 } } { \mu } - \mathrm { M } _ { 1 }$

Answer 2

System does not accelerate it M₂g £ m (M₁+m)g

M₂ £ m (M₁ + m)

or $\mathrm { m } \geq \frac { \mathrm { M } _ { 2 } - \mu \mathrm { M } _ { 1 } } { \mu }$ or $\mathrm { m } \geq \frac { \mathrm { M } _ { 2 } } { \mu } - \mathrm { M } _ { 1 }$