Projectiles A and B are thrown at angles of $$45^{\circ}$$ and $$60^{\circ}$$ with vertical respectively from top of a $$400 \mathrm{~m}$$ high tower. If their ranges and times of flight are same, the ratio of their speeds of projection $$v_A: v_B$$ is :

[Take $$g=10 \mathrm{~ms}^{-2}$$]

If the total energy transferred to a surface in time $$\mathrm{t}$$ is $$6.48 \times 10^5 \mathrm{~J}$$, then the magnitude of the total momentum delivered to this surface for complete absorption will be:

If mass is written as $$m=k \mathrm{c}^{\mathrm{P}} G^{-1 / 2} h^{1 / 2}$$ then the value of $$P$$ will be : (Constants have their usual meaning with $k a$ dimensionless constant)

A block of mass $$1 \mathrm{~kg}$$ is pushed up a surface inclined to horizontal at an angle of $$60^{\circ}$$ by a force of $$10 \mathrm{~N}$$ parallel to the inclined surface as shown in figure. When the block is pushed up by $$10 \mathrm{~m}$$ along inclined surface, the work done against frictional force is :

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