Embibe Experts Solutions for Chapter: Laws of Motion, Exercise 2: Exercise - 2

A fixed wedge with both surfaces inclined at $45°$ to the horizontal as shown in the figure. A particle $P$ of mass $m$ is held on the smooth plane by a light string that passes over a smooth pulley $A$ and attached to a particle $Q$ of mass $3m$ which rests on the rough plane. The system is released from rest. Given that the acceleration of each particle is of magnitude $\frac{g}{5\sqrt{2}}$ then

the tension in the string is :

In the arrangement shown mass of the block $B$ and $A$ are $2 \mathrm{m}$ and, $8 \mathrm{m}$ respectively. Surface between $B$ and floor is smooth. The block $B$ is connected to block $C$ by means of a pulley. If the whole system is released then the minimum value of the mass of the block $C$ so that the block $A$ remains stationary with respect to $B$ is: (Coefficient of friction between $A$ and $B$ is $\mathrm{\mu }$ and pulley is ideal)

A bead of mass $m$ is located on a parabolic wire, equation( $x^2=ay$) with its axis vertical and vertex directed downward as shown in the figure. If the coefficient of friction is $\mathrm{\mu }$, the highest distance above the x-axis at which the particle will be in equilibrium.

In the arrangement shown tension in the string connecting $4 \mathrm{kg}$ and $6 \mathrm{kg}$ masses is

Two blocks of masses $m_1$ and $m_2$ are connected with a massless undeformed spring and placed over a plank moving with an acceleration $a$ as shown in the figure. The coefficient of friction between the blocks and platform is $\mathrm{\mu }$.

A plate of mass $\mathrm{M}$ is moved with constant velocity $\mathrm{v} = 40\mathrm{m}/\mathrm{s}$ against powder of dust particles moving with constant velocity $\mathrm{u} = 40\mathrm{m}/\mathrm{s}$in opposite direction stick to plate as shown. The density of the dust is $\mathrm{\rho }= {10}^{–3} \mathrm{kg}/{\mathrm{m}}^3$ and plate area is $\mathrm{A} = 10{\mathrm{m}}^2$ Find the force $\mathrm{F}$ required to keep the plate moving uniformly.

In the figure, the pulley $P$ moves to the right with a constant speed $u$. The downward speed of $A$ is $v_{\mathrm{A}}$ and the speed of $B$ to the right is $v_{\mathrm{B}}$.

In an imaginary atmosphere, the air exerts a small force $F$ on any particle in the direction of the particle’s motion. A particle of mass $m$ projected upward takes time $t_1$ in reaching the maximum height and $t_2$ in the return journey to the original point. Then