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

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the centre $P$ (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes $2x$ is

A piece of wire is bent in the shape of a parabola $y=k{x}^2$ ($y$-axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$-axis with a constant acceleration $a$. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire from the $y$-axis is

A ball of mass $0.2 \mathrm{kg}$ is thrown vertically upwards by applying a constant force by hand. If the hand moves $0.2 \mathrm{m}$ while applying the force and the ball goes upto $2 \mathrm{m}$ height further, find the magnitude of the force. Consider $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

A block of mass $m$ is connected to another block of mass $M$ by a string (massless). The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest. Then a constant force $F$ starts acting on the block of mass $M$ to pull it. Find the force on the block of mass $m$.

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 respectively. What is the relative vertical acceleration of $A$ with respect to $B$?

(Use $\sin 30°=\cos 60°=\frac{1}{2} \text{and} \sin 60°=\cos 30°=\frac{\sqrt{3}}{2}$)

A particle of mass $m$ is at rest at the origin at time $t=0$. It is subjected to a force $F\left(t\right)=F_0{e}^{–\mathrm{bt}}$ in the $x$-direction. Its speed $v\left(t\right)$ is depicted by which of the following curves?

A mass$m$supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R\mathit{.}$ If the string does not slip on the cylinder, with what acceleration will the mass fall on release ? 

If a spring of stiffness $\text{'}\mathrm{k}\text{'}$is cut into two parts$\text{'}\mathrm{A}\text{'}$and $\text{'}\mathrm{B}\text{'}$ of length ${\mathrm{l}}_{\mathrm{A}}:{\mathrm{l}}_{\mathrm{B}}=2:3$, then the stiffness of spring $\text{'}\mathrm{A}\text{'}$ is given by :