Question

Two blocks of masses $m_1$ and $m_2$ are connected through a massless inextensible string. Block of mass $m_1$ is placed on the fixed rigid inclined surface, while the block of mass $m_2$ is hanging at the other end of the string, which is passing through a fixed massless frictionless pulley shown in figure. The coefficient of static friction between the block and the inclined plane is 0.8. The system of masses $m_1$ and $m_2$ is released from rest. Take $g=10m{s}^{-2}$

• A. The tension in the string is 20 N after releasing the system.
• B. The contact force by the inclined surface on the block is along normal to the inlined surface.
• C. the magnitude of the contact force by the inclined surface on the block $m_1$ is $20\sqrt{3}\text{N}$.
• D. None of these.

Answer 1

Answer: (A), (B), (C)

The correct options are
A The tension in the string is 20 N after releasing the system.
B The contact force by the inclined surface on the block is along normal to the inlined surface.
C the magnitude of the contact force by the inclined surface on the block $m_1$ is $20\sqrt{3}\text{N}$.



Since net pulling force is zero on the system, static friction adjusts its value to zero and net contact force by the incline is perpendicular to the incline.

$m_1\text{g sin}{30}^{\circ }-T-\mu N=m_{1}a$
$N=m_{1}gcos{30}^{\circ }$
$T-m_{2}g=m_{2}a$
$T=20\text{N}$