Newtons 2nd Law Applied to Particles in Rectilinear Motion

Q. A uniform rod of length 'l' is kept vertically on a horizontal smooth surface at a point O. If it is rotated slightly and released, it falls down on the horizontal surface. the lower end will remain

1. at O
2. at a distance less than l/2 from O
3. at a distance l/2 from O
4. at a distance larger than l/2 from O

Q. A man weighing 72.5 kg stands in a boat so that he is 4.58 m from the shore. He walks 2.44 m in the boat towards the shore and then stops. How far from the shore will he be at the end of this time? The boat weighs 90.7 kg, and there is assumed to be no friction between it and the water.

1. 2.14 m
2. 2.41 m
3. 3.22 m
4. 3.5 m

Q. A vehicle of mass 1000 kg moving with a velocity of 10 m/s comes to rest because of a breaking force after transversing a distance of 10 m. The work done on the vehicle is

1. 50 kJ
2. 60 kJ
3. 75 kJ
4. 100 kJ

Q. A particle of mass 5kg moves in a straight line under the influence of a momentum which is varying parabolically, If the rate of change of momentum at t = 0 is 80 N. After 2 second rate of change of momentum is 480 N. What will be the velocity of particle after 5 second when it started from rest from origin ?

1. 580 m/s
2. 330 m/s
3. 680 m/s
4. 250 m/s

Q. If acceleration of an object is given as $a=-6s^{-3}$, where's is the displacement. Motion starts with infinite displacement from rest, then what will be the velocity of the object at 6 m?

1. 0.167 m/s
2. 2.3 m/s
3. 0.408 m/s
4. 0.68 m/s

Q. A bullet after getting fired from a gun goes through a plank of thickness h and changes its velocity from u to v and resisting force is proportional to cube of velocity. The time of motion of the bullet in the plank is proportional to

1. $(u^2-v^2)u^{-2}$
2. $(u-v)(uv{)}^{-1}$
3. $(u^2-v^2)u^{-1}$
4. $(u^2-v^2)(uv{)}^{-2}$