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An observer is located on a horizontal, circular turntable which rotates about a vertical axis passing through its center, with a uniform angular speed of 2 rad/sec. A mass of 10 grams is sliding without friction on the turntable. At an instant when the mass is at a distance of 8 cm from the axis, it is observed to move towards the center with a speed of 6 cm/sec. The net force on the mass, as seen by the observer at that instant, is
  • a)
    0.0024 N
  • b)
    0.0032 N
  • c)
    0.004 N
  • d)
    0.006 N
Correct answer is option 'C'. Can you explain this answer?
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Given information:
- Angular speed of the turntable, ω = 2 rad/sec
- Mass of the sliding object, m = 10 grams = 0.01 kg
- Distance of the mass from the axis, r = 8 cm = 0.08 m
- Speed of the mass towards the center, v = 6 cm/sec = 0.06 m/sec

To find: The net force on the mass, as seen by the observer at that instant.

Formula used:
- Centripetal force, F = mω²r

Calculations:
1. Convert the mass to kg:
Mass, m = 10 grams = 0.01 kg

2. Calculate the centripetal acceleration, a:
Centripetal acceleration, a = ω²r
Substituting the given values:
a = (2 rad/sec)² × 0.08 m = 0.32 m/sec²

3. Calculate the net force, F:
Net force, F = ma
Substituting the given values:
F = (0.01 kg) × 0.32 m/sec² = 0.0032 N

Therefore, the net force on the mass, as seen by the observer at that instant, is 0.0032 N. Hence, the correct answer is option C.
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An observer is located on a horizontal, circular turntable which rotates about a vertical axis passing through its center, with a uniform angular speed of 2 rad/sec. A mass of 10 grams is sliding without friction on the turntable. At an instant when the mass is at a distance of 8 cm from the axis, it is observed to move towards the center with a speed of 6 cm/sec. The net force on the mass, as seen by the observer at that instant, isa)0.0024 Nb)0.0032 Nc)0.004 Nd)0.006 NCorrect answer is option 'C'. Can you explain this answer?
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