The potential energy function for a particle executing linear SHM is given by $$V(x)=\frac{1}{2} k x^2$$ where $$k$$ is the force constant of the oscillator (Fig). For $$k=0.5 \mathrm{~N} / \mathrm{m}$$, the graph of $$V(x)$$ versus $$x$$ is shown in the figure. A particle of total energy $$E$$ turns back when it reaches $$x= \pm x_m$$. If $$V$$ and $$K$$ indicate the PE and KE, respectively of the particle at $$x=+x_m$$, then which of the following is correct?

Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed $$v$$ as shown in figure.

A body of mass 0.5 kg travels in a straight line with velocity $$v=a x^{3 / 2}$$ where $$a=5 \mathrm{~m}^{-1 / 2} \mathrm{~s}^{-1}$$. The work done by the net force during its displacement from $$x=0$$ to $$x=2 \mathrm{~m}$$ is

A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in figure correctly shown the displacement-time curve for its motion?

Which of the diagrams shown in figure most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit?