The displacements of two particles of same ma | vedclass

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

Question

(D) The total energy of a particle executing $SHM$ is given by $E = \frac{1}{2} m \omega^2 A^2$,where $m$ is the mass,$\omega$ is the angular frequenc

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(D) The total energy of a particle executing $SHM$ is given by $E = \frac{1}{2} m \omega^2 A^2$,where $m$ is the mass,$\omega$ is the angular frequency,and $A$ is the amplitude.For the first particle,$x_1 = 4 \sin \left(10 t + \frac{\pi}{6}ight)$,the angular frequency $\omega_1 = 10 	ext{ rad/s}$ and amplitude $A_1 = 4 	ext{ units}$.Thus,$E_1 = \frac{1}{2} m (10)^2 (4)^2 = \frac{1}{2} m (100)(16) = 800m$.For the second particle,$x_2 = 5 \cos (\omega t)$,the angular frequency is $\omega$ and amplitude $A_2 = 5 	ext{ units}$.Thus,$E_2 = \frac{1}{2} m \omega^2 (5)^2 = \frac{25}{2} m \omega^2$.Given that the energies are equal,$E_1 = E_2$.$800m = \frac{25}{2} m \omega^2$.$1600 = 25 \omega^2$.$\omega^2 = \frac{1600}{25} = 64$.$\omega = 8 	ext{ units}$.

The displacements of two particles of same mass executing $SHM$ are represented by the equations $x_1 = 4 \sin \left(10 t + \frac{\pi}{6}\right)$ and $x_2 = 5 \cos (\omega t)$. The value of $\omega$ for which the energies of both the particles remain same is (in $\text{ unit}$)

Similar Questions

When acetaldehyde is reacted with $LiAlH_4$,what is the product formed?

In the figure, a potential of $+1200 \, V$ is applied to point $A$ and point $B$ is earthed. What is the potential at point $P$ (in $V$)?

Which of the following noble gases has the highest polarizability?

Consider the situation shown in the figure. The wire $AB$ is sliding on the fixed rails with a constant velocity $v$. If the wire $AB$ is replaced by a semicircular wire of the same chord length,the magnitude of the induced current will

$A$ particle of mass $2\, kg$ is initially at rest. $A$ force acts on it whose magnitude changes with time. The force-time graph is shown below. The velocity of the particle after $10\, s$ is ......... $ms^{-1}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module