Embibe Experts Solutions for Exercise 7: Assignment

A smooth massless horizontal rod $PQ$ is free to rotate about a vertical axis through end $P.$ The rod is filled with a small sized sleeve of mass $m$ connected to the end $P$ by an ideal spring of length $L_0$ and force constant $k.$ The work performed to slowly increase the angular velocity to the value $\sqrt{\frac{k}{2m}}$ is $\frac{pk{L}_0^2}{4}.$ The value of $p$ is

Displacement-time equation of two particles moving along $x$-axis are $x_1=4+4 \mathrm{sin\omega }t$ and $x_2=3 \mathrm{cos\omega }t$ where $\mathrm{\omega }=\mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{–1}.$ Maximum separation will be at time $t$ equal to

Consider the shown diagram. All pulleys are massless and frictionless, springs are ideal and all connecting strings are ideal. Find the natural frequency of the system shown in figure

Blocks $P$ and $Q$ of masses $m$ and $3m$ are connected by a spring of force constant $k.$ The system is placed on a smooth horizontal surface. At time $t=0$, block $P$ is projected horizontally with velocity $V_0$ towards right. Then

The energy of a particle executing simple harmonic motion is given by $E=A{x}^2+B{v}^2$, where $x$ is displacement from mean position $x=0$ and $v$ is the velocity of particle at displacement $x$, then choose the correct statement(s).

In the figure shown, pulleys, string and springs are ideal. The natural frequency of oscillation is given as $\frac{1}{\pi }\sqrt{\frac{k}{nm}}.$ The value of $n$ is

A block of mass $5 \mathrm{kg}$ executes SHM under the restoring force of a spring on a smooth horizontal surface. The amplitude and time period of the motion are $1 \mathrm{m}$ and $\pi \mathrm{s}$ respectively. Maximum force exerted by spring on the block is $x \mathrm{N}.$ Find the value of $x.$

Consider the shown arrangement. Rod is massless which can rotate freely about hinge $O.$ All the springs are ideal and massless. If frequency of small oscillations of block $m$ (Neglect gravity) is $f=\frac{1}{2\pi }\sqrt{\frac{Nk}{9m}}$, then find value of $N.$