Our Pick(s) Job begins : 08 Oct 20, See the solutions : 09 Oct 20
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1. A ℓ long rope protrudes from a U-shaped, narrow, small, fixed tube facing downwards, as shown. Initially, the rope is ℓ / 2 long on both sides. Here it is in an unstable equilibrium position as the friction is negligible.
a) If the rope starts to slide to one side, what will be its speed by which time will it straighten?
b) What is the speed of the rope when the instantaneous center of mass of the rope is just at the same height as the end of the upward sliding piece of rope?
2. At what angle do we have to throw a ball from the bottom of a slope with
a slope of 300 if we want it to rise vertically after an elastic collision with the slope?
3. A slope with a quarter-circular
cross-section and a radius R = 0.5 m, tangentially connected to a plank, weighing M = 6 kg(together with the structure of circular cross section), as
shown in the figure. From a height h = 1.5 m from the top of the slope, a body
of negligible size weighing m = 3 kg falls on the slope, through which it
slides without friction.
a. At what maximum force does the if the plank can move freely without friction?
b. What is the radius of curvature of the trajectory of the ball relative to the plank at the bottom of the arc?