Two projectiles P₁ and P₂ thrown with speed in the ratio $$\sqrt3$$ : $$\sqrt2$$, attain the same height during their motion. If P₂ is thrown at an angle of 60$$^\circ$$ with the horizontal, the angle of projection of P₁ with horizontal will be :

An air bubble of negligible weight having radius r rises steadily through a solution of density $$\sigma$$ at speed v. The coefficient of viscosity of the solution is given by :

A 2 kg block is pushed against a vertical wall by applying a horizontal force of 50 N. The coefficient of static friction between the block and the wall is 0.5. A force F is also applied on the block vertically upward (as shown in figure). The maximum value of F applied, so that the block does not move upward, will be :

(Given : g = 10 ms^$$-$$2)

Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energies will be :