Question

The masses $4m$ and $m$ are connected by a light string passing over a frictionless pulley fixed at inclined plane of inclination 45${}^{\circ }$ as shown in figure. The coefficient of friction between $4m$ and inclined plane is $\frac{1}{\sqrt{2}}$. When two blocks are released, then

• A. the tension in the string is mg
• B. the frictional force on the block of 4m will be 2mg.
• C. the block of m will move in upward direction.
• D. the frictional force on block of mass 4m has magnitude $(2\sqrt{2}-1)$ mg.

Answer 1

Answer: (A), (D)

The correct options are
A the tension in the string is mg
D the frictional force on block of mass 4m has magnitude $(2\sqrt{2}-1)$ mg.

Maximum value of friction force between 4m and inclined plane
$=\mu \left(4mg\right)cos45$
$=\frac{1}{\sqrt{2}}\left(4mg\right)\frac{1}{\sqrt{2}}=2mg$
Here pulling force
$F_p=$ 4mg sin 45 - mg
$=(2\sqrt{2}-1)mgwhichis<2mg$
$\therefore$ Block will not move.
$\therefore$ Acceleration of 4m block
$=0,T=mg$
$\therefore$ frictional force on 4m block
$(2\sqrt{2}-1)mg$