$\lambda \propto V \propto \sqrt{\frac{T}{\mu}}$
New $\frac{\lambda^{\prime}}{\lambda}-\frac{\sqrt{2 T}}{\sqrt{T}} \Rightarrow \lambda^{\prime}=\sqrt{2} \lambda$
$\frac{\lambda^{\prime}}{2}=\sqrt{2} \cdot \frac{\lambda}{2}=\sqrt{2} \mathrm{x}$ Ans.
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$1.$ The phase space diagram for a ball thrown vertically up from ground is
mcq $Image$
$2.$ The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $E_1$ and $E_2$ are the total mechanical energies respectively. Then $Image$
$(A)$ $ E_1=\sqrt{2} E_2$ $(B)$ $ E_1=2 E_2$
$(C)$ $ E_1=4 E_2$ $(D)$ $ E_1=16 E_2$
$3.$ Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is $Image$
mcq $Image$
Give the answer question $1,2$ and $3.$
$\theta = 2{t^3} + 0.5,$
where $\theta $ is in radians and $t$ is in second. Then the angular velocity of the particle after two second will be ....... $rad/sec$