The velocity at the mean position of a partic | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The velocity of a particle in $S.H.M.$ at the mean position is given by $v = a\omega$,where $a$ is the amplitude and $\omega$ is the angular frequ

Vedclass · Accepted Answer

$\frac{\sqrt{3}}{2}v$

Vedclass · Answer

(C) The velocity of a particle in $S.H.M.$ at the mean position is given by $v = a\omega$,where $a$ is the amplitude and $\omega$ is the angular frequency.At a distance $y = \frac{a}{2}$,the velocity $v'$ is given by the formula $v' = \omega \sqrt{a^2 - y^2}$.Substituting $y = \frac{a}{2}$ into the formula:$v' = \omega \sqrt{a^2 - (\frac{a}{2})^2}$$v' = \omega \sqrt{a^2 - \frac{a^2}{4}}$$v' = \omega \sqrt{\frac{3a^2}{4}}$$v' = \frac{\sqrt{3}}{2} a\omega$Since $v = a\omega$,we have $v' = \frac{\sqrt{3}}{2} v$.

The velocity at the mean position of a particle executing $S.H.M.$ is $v$. What is the velocity of the particle at a distance equal to half of the amplitude?

Similar Questions

Which of the following does not produce $NO_2$ gas with concentrated $HNO_3$?

Which one of the following exhibits enantiomerism?

Two batteries,one of $emf$ $18 \, V$ and internal resistance $2 \, \Omega$ and the other of $emf$ $12 \, V$ and internal resistance $1 \, \Omega$,are connected in parallel as shown in the figure. The voltmeter $V$ will record a reading of ............. $V$.

$A$ car is moving with a speed of $72 ~km/h$ towards a hill. The car blows its horn at a distance of $1800 ~m$ from the hill. If the echo is heard after $10 ~s$,what is the speed of sound in $m/s$?

$A$ disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. The disc is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter is

Vedclass Test Series

Exam Paper Generator

Online Exam Module