Question

Q17. A metallic sphere of mass 1kg and radius 5 cm is welded to the end B of a thin rod AB of length 50 cm and mass o.5 kg as shown. Find the center of the mass of the system by considering origin as the center of the rod? A) 35 cm B) 20 cm C) 45cm D) 48cm E1 25 cm A. Q18. Two children, Anne and Jack, ride on a merry-go-round. Anne is at a greater distance from the axis of rotation than Jack. Which of the following is true? A) Jack and Anne have the same tangential speed and acceleration. B) Jack has a greater angular speed and acceleration than Anne. C) Jack has a smaller angular speed and acceleration than Anne D) Anne has a smaller tangential speed and acceleration than Jack. E) Jack and Anne have the same angular speed and acceleration. 019. Two solid cylinders are rotating about an axis that passes through the center of both ends of each cylinder. Cylinder A has half the mass and twice the radius of cylinder B, but they have the same rotational kinetic energy. What is the ratio of the angular velocities,B,for these two cylinders? Take the moment of Inertia for a solid cylinder as MR2, with mass M and radius R. A) 0.28 B) 071 c) 0.50 D) 10 4.0 020. Swimmers at a water park have a choice of two frictionless water slides as shown in the figure. Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, d ropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the end of slide compares with v2, the speed of a swimmer reaching the end of slide 2 and compare time taken to reach the water respectively? A)v1 >v2 and t-t2 B) v1 < 2 and tt C)v1-v2 and tot D) 1 v2 and t-t E) No simple relationship exists between v1 and v2 because we do not know the curvature of slide 2. Q21. Mary is riding a roller coaster. Her mother who is standing on the ground behind her yells out to her at a frequency of 1000 Hz, but it sounds like 920 Hz. V 343 m/s). Which one is correct about the problem and Mary's speed? A) Moving observer away from the source with the speed 27.4 m/s B) Moving source away from the observer with the speed 2.74 m/s C) Moving source towards the observer with the speed 27.4 m/s D) Moving observer towards the source with the speed 27.4 m/s E) Moving observer away from the source with the speed 2.74 m/s

Answer 1

Answers:. 17). B

18). B

19). B

20). C

21). A

B 18). B 19). B 20). C 21). A A rightarrow Anne J rightarrow Jack From the given data r_A > r_J By conservation of angular momentum L = Iw = mr^2 w Here L and m are constant So w alpha 1/r^2 = > r_A > r_J w_A < w_J Therefore w_J > w_A Therefore Ans: [B] KE_rotational = 1/2 Iw^2 = 1/2 1/2 MR^2 middot w^2 Here KE_rotational = Constant Therefore w^2 alpha 1/MR^2 = > (w_1/w_2)^2 = M_2/m_1 middot (R_2/R_1)^2 (w_1/w_2)^2 = M/M/2 middot (r/2r)^2 = 2/1 times 1/4 = 1/2 (w_1/w_2)^2 = 0.5 = > w_1/w_2 = 1/squareroot 2 w_1/w_2 = 1/squareroot 2 times squareroot 2/squareroot 2 = 1.414/2 = 0.707 Therefore w_1/w_2 = 0.71 Ans: (B) By law of conservation of energy Total energy at A = Total energy at B mg h + 1/2 m U^2 = mg (0) + 1/2 mv^2_1 mg h + 0 = 1/2 mv^2_1 Therefore v_1