Embibe Experts Solutions for Exercise 6: Assignment Set-2

$1 \mathrm{kg}$ block performs vertical harmonic oscillations with amplitude $1.6 \mathrm{cm}$ and frequency $25 \mathrm{rad} s^{-1}$. The maximum value of the force that the system exerts on the surface is$11n \mathrm{N}$. Value of $n$, is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2},{\mathrm{\pi }}^2=10\right)$

The time period of a particle in$\mathrm{SHM}$ is $8\mathit{ }s$. At $t=0$, it is at mean position. The ratio of the displacement travelled by it in $1^{\text{st }}$ and $2^{\text{nd }}$ second

is$\frac{1}{\sqrt{n}-1}·$ Value of $n$, is

$T_1$ is the time period of a simple pendulum. The point of suspension is moved vertically upwards according to $y=k{t}^2\left(k=1{ \mathrm{ms}}^{-2}\right)$. New period is $T_2$. Now $\frac{T_1^2}{T_2^2}$ is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A particle is executing$\mathrm{SHM}$ according to the equation $x=A\mathrm{sin\omega }t$. Average speed of the particle during the interval $0\le t\le \frac{\mathrm{\pi }}{6\mathrm{\omega }}$ $\frac{nA\mathrm{\omega }}{\mathrm{\pi }}$. Value of $n$, is

Two particles undergo $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ along parallel lines with the same time period $\left(T\right)$ and equal amplitudes. At a particular instant one particle is at its extreme position while the other is at its mean position. They move in the same direction. They will cross each other after a further time $\frac{nT}{8}$. Value of $n$, is -------.

A thin square plate of mass $m$ and side $a$ is hinged about $AB$ so as to execute small oscillations about $AB$. The time period of oscillations is $\mathrm{\pi }\sqrt{\frac{na}{3g}}$. Value of $n$, is

A uniform disc of radius $R$  is pivoted about point $P$ such that it is free to oscillate in the vertical plane. Distance between the pivot and centre of disc $x$, such that the time period of oscillation is minimum, is $\frac{R}{\sqrt{n}}$. Value of $n$, is

A torsional pendulum consists of a uniform disc of mass $m$ and radius $R$. String has torsional constant $C$ and passes through central vertical axis of the disc. Time period of this torsional pendulum is raised to twice of its original when a concentric ring of radius $R$ is glued with the disc. Mass of the ring is $nm$. Value of $n$, is