Question

Blocks of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of massless, inextensible string and a frictionless pulley as shown. The wedge is inclined at 45° to horizontal on both sides. The coefficient of friction between block A and wedge is 2/3 and that between block B and wedge is 1/3. If system of A and B is released from rest then acceleration of A is

• A. Zero
• B. 1 ms^-2
• C. 2ms^-2
• D. 3ms^-2

Answer 1

Answer: (A)

Zero

Answer 2

f_max for A = μ₁(mg cos 45⁰)

= $\frac { 2 } { 3 } \frac { \mathrm { mg } } { \sqrt { 2 } } = \frac { \sqrt { 2 } } { 3 } \mathrm { mg }$

Also f_max for B = μ₂(2mg cos 45)

= 1/3 (2mg $\sqrt { 2 }$ ) = $\sqrt { 2 } / 3$ mg

Total frictional force

= $\frac { \sqrt { 2 } } { 3 } \mathrm { mg } + \frac { \sqrt { 2 } } { 3 } \mathrm { mg } = \frac { 2 \sqrt { 2 } } { 3 } \mathrm { mg }$ But pulling force

= F₁ – F₂ = $\frac { 2 \mathrm { mg } } { \sqrt { 2 } } - \frac { \mathrm { mg } } { \sqrt { 2 } } = \frac { \mathrm { mg } } { \sqrt { 2 } }$