Embibe Experts Solutions for Chapter: Laws of Motion, Exercise 3: Exercise-3

A system consists of three masses $m_1\text{,} m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_3$ hangs freely and $m_2$ and $m_1$ are on a rough horizontal table (the coefficient of friction$=\mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is (assume, $m_1=$$m_2=m_3=m$),

Three blocks with masses $m\text{,} 2m$ and $3m$ are connected by strings as shown in the figure. After an upward force $F$ is applied on block $m$, the masses move upward with constant speed $v$. What is the net force on the block of mass $2m$? $(g$ is the acceleration due to gravity)

Three blocks $A\text{,} B$ and $C$ of masses $4 \mathrm{kg}\text{,} 2 \mathrm{kg}$ and $1 \mathrm{kg}$, respectively, are in contact on a frictionless surface as shown. If a force of $14 \mathrm{N}$ is applied on the $4 \mathrm{kg}$ block, then the contact force between $A$ and $B$ is,

Two blocks $A$ and $B$ of masses $3m$ and $m$, respectively, are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of $A$ and $B$ immediately after the string is cut are, respectively,

A block of mass $m$ is placed on a smooth inclined wedge $ABC$ of inclination $\theta$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $\theta$ for the block to remain stationary on the wedge is,

Two fixed frictionless inclined planes making an angle $30°$ and $60°$ with the vertical are shown in the figure. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$?

A mass of $10 \mathrm{kg}$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the mass, the rope deviated at an angle of $45°$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (Take, $g=10 {\mathrm{ms}}^{-2}$ )

Two forces $P$ and $Q$ of magnitude $2F$ and $3F$, respectively, are at an angle $\mathrm{\theta }$ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $\mathrm{\theta }$ is