Two particles. A and B, are in uniform circular motion about a common center. Th

Question

Two particles. A and B, are in uniform circular motion about a common center. The acceleration of particle A is 8.5 times that of particle B. The period of particle B is 2.0 times the period of particle A. The ratio of the radius of the motion of particle A to that of particle B is closest to (a) R_A/R_B = 2.1 (b) R_A/R_B = 4.3 (c) R_A/R_B = 18 (d) R_A/R_B = 0.24 (e) R_A/R_B = 17 A speed-skater is moving counterclockwise around a circular track of radius R = 50 m. The skater's mass is m = 80 kg. A frictional force is directed opposite to the direction of motion, characterized by a coefficient of kinetic friction mu _k = 0.05 between the ice surface and the metal skate blades. The skater is observed coming to a complete stop, her speed decreasing from v = 5 m/s to zero over a distance delta s. Which of the following statements is incorrect? (a) The force due to friction is f_k = mu _k mg = 40 N (b) The acceleration is a = squareroot mu^2 _k g^2 + v^4/R^2 = 0.7 m/s^2. directed behind and to the left of the skater. (c) The stopping distance is delta s = v^2/2 mu _kg = 30 m (d) The original speed v = 5 m/s corresponds to an angular frequency omega = v/2 pi R = 0.02 rad/s A child on a carousel travels in a circular path at constant angular frequency omega. The pony he's riding is a distance R = 12 m from the axis of rotation (at the center of the circle). Every T = 15 s he returns to the same point. Which of the following is a correct statement? (a) The child's speed is v = 2 pi R/T = 5.0 m/s (b) The child experiences no acceleration. (c) The child experiences a centripetal acceleration a = 4 pi^2R/T = 1.1 m/s^2 directed outward, away from the axis of rotation The blade in a blender starts at rest. It then pulses-i e.. it spins up and spins down, coming back to rest. Over the first two seconds, the blade undergoes angular acceleration alpha _1 = + 2.0rad/s^2 over the next four seconds, it undergoes angular deceleration alpha _ 2 = 1.0 rad/s^2 How much has the blade rotated after the six-second pulse is complete? Write your answers directly in the boxes below. A projectile is launched with velocity v = 60.0 m/s at an angle theta = 30 degree above the horizontal. What is its maximum height neglecting drag forces? (a) 34 m (b) 38 m (c) 42 m (d) 46 m (e) 50 m

Explanation / Answer

Q. 8

v = 2pir / T

A= v^2 / r = 4 pi^2 r / T^2

Aa = 8.5 (Ab), Tb = 2 (Ta)

Aa / Ab = Rb Ta^2/ Tb^2 Ra

8.5 x 4 = Rb/ Ra

option D ( 0.24)

Q.9 ( correct option is c , as it;'s a wrong calculation)

Q.10 ( correct option is a)

Q;12 max height = ( 60 sin 30)^2/ 2g = 46 m apprx

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