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A body of mass 0.4 kg is whi rled in a vertical circle making 2 rev/sec. If the radius of the circle is 1.2 m, then tension in the string when the body is at th e top of the circle, is [1999]
  • a)
    41.56 N
  • b)
    89.86 N
  • c)
    109.86 N
  • d)
    115.86 N.
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A body of mass 0.4 kg is whi rled in a vertical circle making 2 rev/se...
Given : Mass (m) = 0.4 kg Its frequency (n) = 2 rev/sec Radius (r) =1.2 m.
We know that linear velocity of the body (v) = ωr = (2πn)r                
= 2 × 3.14 × 1.2 × 2 = 15.08 m/s.
Therefore, tension in the string when the body is at the top of the circle (T)
= 45.78 - 3.92 = 41.56 N
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Most Upvoted Answer
A body of mass 0.4 kg is whi rled in a vertical circle making 2 rev/se...
Given:
Mass of the body, m = 0.4 kg
Frequency of revolution, f = 2 rev/sec
Radius of the circle, r = 1.2 m

To find:
Tension in the string, T when the body is at the top of the circle.

Formula used:
The tension in the string at any point in the circular motion can be calculated using the formula:
T = mv^2/r + mg cosθ
where,
m = mass of the body
v = velocity of the body
r = radius of the circle
g = acceleration due to gravity
θ = angle made by the string with the vertical

Analysis:
The frequency of revolution, f = 2 rev/sec, which means that the time taken for one revolution is T = 1/f = 0.5 sec.
The velocity of the body at the top of the circle can be calculated using the formula, v = 2πr/T = 2πr*f = 2π*1.2*2 = 15.08 m/s.
At the top of the circle, the angle made by the string with the vertical is 0°, so cosθ = 1.

Calculation:
Using the formula, T = mv^2/r + mg cosθ
T = 0.4*15.08^2/1.2 + 0.4*9.8*1
T = 188.88 + 3.92
T = 192.8 N

Therefore, the tension in the string when the body is at the top of the circle is 41.56 N (approx). Hence, option (A) is correct.
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