Question

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

• 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:
$F_P=4mgcos45-mg$
$=(2\sqrt{2}-1)mg<2mg$

$\therefore$ Block will not move.
$\therefore$ Acceleration of $4m$ block $=0$, $T=mg$
$\therefore$ Frictional force on $4m$ block $=(2\sqrt{2}-1)mg$