ABCDE is a smooth iron track in the vertical plane. The sections ABC a

1.	ABCDE is a smooth iron track in the vertical plane. The sections ABC and CDE are quarter circles. Points B and D are very close to C. M is a small magnet of mass m. The force of attraction between M and the track is F, which is constant and always normal to the track. M starts from rest at A.(a) If M is not leave the track at C then F ≥ 2mg. (b) At B, the normal reaction of the track is F - 2mg. (c) At D, the normal reaction of the track is F + 2mg. (d) The normal reaction of the track is equal to F at some point between A and B.
Answer» Correct Answer sis: (a, b, c, & d) At C, 1/2 mv² = mgr or mv²/r = 2mg. If N = the normal reaction of the track, F - N = mv²/r = 2mg or F = N + 2mg. As N ≥ 0, F ≥ 2mg Taking the speeds at B and D to be the same as at C, at B, F - N = 2mg or N = F - 2mg (Centre of curvature is O.) at D, N - F = 2mg or N = F + 2mg (Centre of curvature is O'.) For ∠AOM = θ, mg(r - rcos θ) = 1/2 mv² or mv²/r = 2mg (1 - cos θ) or 2mg (1 - cos θ) = mgcos θ + F - N. For F = N, cos θ = 2/3.

ABCDE is a smooth iron track in the vertical plane. The sections ABC and CDE are quarter circles. Points B and D are very close to C. M is a small magnet of mass m. The force of attraction between M and the track is F, which is constant and always normal to the track. M starts from rest at A.(a) If M is not leave the track at C then F ≥ 2mg. (b) At B, the normal reaction of the track is F - 2mg. (c) At D, the normal reaction of the track is F + 2mg. (d) The normal reaction of the track is equal to F at some point between A and B.

Answer»

Correct Answer sis: (a, b, c, & d)

At C, 1/2 mv² = mgr or mv²/r = 2mg.

If N = the normal reaction of the track,

F - N = mv²/r = 2mg or F = N + 2mg.

As N ≥ 0, F ≥ 2mg

Taking the speeds at B and D to be the same as at C,

at B, F - N = 2mg or N = F - 2mg (Centre of curvature is O.)

at D, N - F = 2mg or N = F + 2mg (Centre of curvature is O'.)

For ∠AOM = θ,

mg(r - rcos θ) = 1/2 mv² or mv²/r = 2mg (1 - cos θ)

or 2mg (1 - cos θ) = mgcos θ + F - N.

For F = N, cos θ = 2/3.