A bob of heavy mass $m$ is suspended by a light string of length $/$. The bob is given a horizontal velocity $v_0$ as shown in figure. If the string gets slack at some point $P$ making an angle $\theta$ from the horizontal, the ratio of the speed $v$ of the bob at point $P$ to its initial speed $v_0$ is:

An object moving along horizontal $$x$$-direction with kinetic energy $$10 \mathrm{~J}$$ is displaced through $$x=(3 \hat{i}) \mathrm{m}$$ by the force $$\vec{F}=(-2 \hat{i}+3 \hat{j}) \mathrm{N}$$. The kinetic energy of the object at the end of the displacement $$x$$ is

An object falls from a height of $$10 \mathrm{~m}$$ above the ground. After striking the ground it loses $$50 \%$$ of its kinetic energy. The height upto which the object can rebounce from the ground is:

At any instant of time $$t$$, the displacement of any particle is given by $$2 t-1$$ ($$\mathrm{SI}$$ unit) under the influence of force of $$5 \mathrm{~N}$$. The value of instantaneous power is (in $$\mathrm{SI}$$ unit):