A 1.00 times 10^{-20} ,kg particle is vibrati | vedclass

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

Question

(A) Given:Mass $m = 1.00 	imes 10^{-20} \,kg$Period $T = 1.00 	imes 10^{-5} \,s$Maximum speed $v_{max} = A \omega = 1.00 	imes 10^3 \,m/s$Angular f

Vedclass · Accepted Answer

$1.59$

Vedclass · Answer

(A) Given:Mass $m = 1.00 	imes 10^{-20} \,kg$Period $T = 1.00 	imes 10^{-5} \,s$Maximum speed $v_{max} = A \omega = 1.00 	imes 10^3 \,m/s$Angular frequency $\omega$ is given by:$\omega = \frac{2\pi}{T} = \frac{2\pi}{1.00 	imes 10^{-5}} = 2\pi 	imes 10^5 \,rad/s$Using the formula for maximum speed:$v_{max} = A \omega$$1.00 	imes 10^3 = A 	imes (2\pi 	imes 10^5)$Solving for amplitude $A$:$A = \frac{1.00 	imes 10^3}{2\pi 	imes 10^5} = \frac{1}{2\pi} 	imes 10^{-2} \,m$$A \approx 0.15915 	imes 10^{-2} \,m = 1.5915 	imes 10^{-3} \,m$Since $1 \,m = 1000 \,mm$:$A = 1.5915 	imes 10^{-3} 	imes 10^3 \,mm = 1.5915 \,mm$Rounding to two decimal places,$A = 1.59 \,mm$.

$A$ $1.00 \times 10^{-20} \,kg$ particle is vibrating under simple harmonic motion with a period of $1.00 \times 10^{-5} \,s$ and with a maximum speed of $1.00 \times 10^3 \,m/s$. The maximum displacement of the particle from the mean position is .......... $mm$.

Similar Questions

The maximum velocity and the maximum acceleration of a body moving in a simple harmonic oscillator are $2 \ m/s$ and $4 \ m/s^2$,respectively. Then the angular velocity will be ..... $rad/s$.

The displacement of a particle in $S.H.M.$ is given by $x = A \cos(\omega t + \pi/6)$. At what time will its speed be maximum?

From the given displacement-time graph of an oscillating particle,find the maximum velocity of the particle.

$A$ particle executes linear simple harmonic motion with an amplitude of $3\,cm$. When the particle is at $2\,cm$ from the mean position,the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:

The maximum speed of a particle executing $S.H.M.$ is $1 \ m/s$ and its maximum acceleration is $1.57 \ m/s^2$. The time period of the particle will be .... $s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module