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 0.5 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 E) 25 em 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. wWhich 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, afos, for these two cylinders? Take the moment of inertia for a solid cylinder as MRe, with mass M and radius R. A) 0.28 B) 071 C 050D) 1.0E) 40 020. Swinsmers at a water park have a choice of two frictionless water slides as shown in the figure. Althouigh both slides drop over the same height, k, slide I is straight while slide 2 is curved, dropping first and then leveling outB How does D1 of a swimmer reaching the end of slide 1 compares with #2, the speed of a swimmer reaching the end of slide 2 and compare time taken to reach the waber respectively? B) 01 12 and tbt C)1- 2 and tot D)12 and t E) No simple relationship exists between and F2 because we do not know the curvature of slide 2 Q21. Mary is riding a roler coaster. Her mother who is standing on the ground behind her yells out to ber at a frequency of 1000 Hs but it sounds like 920 Hz(nd343 m/s). Which one is correct about the problem and Mary's speedi A) Moving observer away from the source with the speed 27.4 m/s 8) Moving seurce 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

Here we will use result for finding centr of mass of multiple element system.

Here we will use result for finding center of mass of multiple element system. X_cm = m_1 x_1 + m_2 x_3 + /m_1 + m_2 x_cm = (0.5) (0.1) + (1) (25 + 5)/(0.5 + 1) = 30/1.5 = 20 cm so option (B) is correct They have same angular speed and acceleration has greater tangential speed any and acceleration. So option (E) is correct I_A = (M/2) (2R^2)/2 I_B = (M) (r)^2/2 K middot E_A = 1/2 I_A w^2_A K middot E_A = 1/2 I_A omega^2_A K middot E_A = K middot E_B 1/2 (M/2) 4R^2/2 omega^2_A = 1/2 MR^2/2 omega^2_B omega^2_A = 1/2 omega^2_b omega_A/ omega_B = 1/squareroot 2 = 1/1.414 = 0.71 option (B) is correct v_1 = v_2, t_1 > t_2 option (c) both have same speed because loss in potential energy is same in both cases.