Two bodies of mass $$1 \mathrm{~kg}$$ and $$3 \mathrm{~kg}$$ have position vectors $$\hat{i}+2 \hat{j}+\hat{k}$$ and $$-3 \hat{i}-2 \hat{j}+\hat{k}$$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

In two different experiments, an object of mass $$5 \mathrm{~kg}$$ moving with a speed of $$25 \mathrm{~ms}^{-1}$$ hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following :

A body of mass $$10 \mathrm{~kg}$$ is projected at an angle of $$45^{\circ}$$ with the horizontal. The trajectory of the body is observed to pass through a point $$(20,10)$$. If $$\mathrm{T}$$ is the time of flight, then its momentum vector, at time $$\mathrm{t}=\frac{\mathrm{T}}{\sqrt{2}}$$, is _____________.

[Take $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$ ]

A ball of mass $$0.15 \mathrm{~kg}$$ hits the wall with its initial speed of $$12 \mathrm{~ms}^{-1}$$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is $$100 \mathrm{~N}$$, calculate the time duration of the contact of ball with the wall.