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Grade: 11

                        

A solid sphere of mass m and radius r is projected horizontally out of a cannon without spinning with an initial speed v 0 . The sphere immediately lands on a level surface, where it skips a few times but eventually begins to roll without slipping. (a) To find the final speed of the sphere, one must apply (A) conservation of energy. (B) conservation of linear momentum. (C) conservation of angular momentum. (D) at least two of the previous principles. (b) The final speed for the sphere depends on (A) the radius. (B) the mass. (C) both the mass and the radius. (D) neither the mass nor the radius.

5 years ago

Answers : (1)

Kevin Nash
askIITians Faculty
332 Points
							(a) The correct option is (A) conservation of energy.
Let the initial kinetic Ki energy of the ball is, Ki = ½ mv0 2
Here v0 is the initial velocity of the solid sphere and m is the mass of the solid sphere.
After the sphere immediately lands on a level surface, where it eventually begins to roll without slipping, the final kinetic energy will be the sum of final linear kinetic energy (=1/2 mv2) having velocity v and rotational kinetic energy Krot.
234-1267_1.JPG
From the above observation, we noticed, the equation v = 5/7 v0 signifies that, the final speed of the solid sphere will only depend upon the initial speed of the sphere. Therefore the final speed for the sphere depends on neither the mass nor the radius. Thus option (D) is correct.
5 years ago
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