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A parent pushes a balanced frictionless playground merry-go- round. The parent exerts a force tangent to the merry-go- round resulting in a torque of 240 N· m; the distance between the center of the merry-go-round and the point of application of the force is 1.6 m. (a) Is the merry-go-round in equilibrium? (A) Yes, for both translational and rotational motion (B) Only for translational motion (C) Only for rotational motion (D) No, not for translational or rotational motion (b) What, if any, is the magnitude of the horizontal force exerted by the merry-go-round axle on the merry-go-round? (A) 384 N (B) 240 N (C) 150 N (D) There is no force.

A parent pushes a balanced frictionless playground merry-go- round. The parent exerts a force  tangent to the merry-go- round resulting in a torque of 240 N· m; the distance between the center of the merry-go-round and the point of application of the force is 1.6 m.
(a) Is the merry-go-round in equilibrium?
(A) Yes, for both translational and rotational motion
(B) Only for translational motion
(C) Only for rotational motion
(D) No, not for translational or rotational motion
(b) What, if any, is the magnitude of the horizontal force exerted by the merry-go-round axle on the merry-go-round?
(A) 384 N        (B) 240 N
(C) 150 N        (D) There is no force.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
6 years ago
233-604_1.PNG
Assume that the axle of the merry-go-round is stationary.
(a) Because there is no friction between the axle of the merry-go-round and the merry-go-round, the merry-go-round can rotate freely about its axle. Therefore there is no rotational equilibrium in merry-go-round but there is translational equilibrium.
Hence, (B) is the correct option.
(b) As explained above, the absence of the friction between the axle and the merry-g-round avoids forces to exist between the axle and the merry-go-round.
Therefore the correct option is (D), while the others are ruled out.

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