The force F acting on a particle of mass m is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is :

A projectile is fired from the surface of the earth with a velocity of 5 m s^$$-$$1 and angle $$\theta $$ with the horizontal. Another projectile fired from another planet with a velocity of 3 m s^$$-$$1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in m s^$$-$$2) is
(Given g = 9.8 m s^$$-$$2)

A particle is moving such that is position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m)
at time t = 2 s and (13 m, 14 m) at time t = 5 s.

Average velocity vector $$\left( {{{\overrightarrow v }_{av}}} \right)$$ from t = 0 to t = 5 s is

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s^$$-$$2 is