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A mass of 1 kg is suspended by a thread. It is (i) lifted up with an acceleration 4.9 m/s2, (ii) lowered with an acceleration 4.9 m/s2.The ratio of the tensions is [1998]
  • a)
    3 : 1
  • b)
    1 : 2
  • c)
    1 : 3
  • d)
    2 : 1
Correct answer is option 'A'. Can you explain this answer?
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A mass of 1 kg is suspended by a thread. It is (i) lifted up with an a...
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A mass of 1 kg is suspended by a thread. It is (i) lifted up with an a...
Solution:

Given, mass of the object (m) = 1 kg
Acceleration due to gravity (g) = 9.8 m/s²
Acceleration of lifting and lowering the mass (a) = 4.9 m/s²

Let T1 and T2 be the tensions in the thread while lifting and lowering the mass respectively.

When the mass is lifted up:
The forces acting on the mass are:
- T1 - tension force acting upwards
- mg - weight of the mass acting downwards

Using Newton's second law of motion,
T1 - mg = ma
T1 - m(g + a) = 0
T1 = m(g + a) ----(1)

When the mass is lowered:
The forces acting on the mass are:
- T2 - tension force acting downwards
- mg - weight of the mass acting downwards

Using Newton's second law of motion,
T2 - mg = -ma
T2 - m(g - a) = 0
T2 = m(g - a) ----(2)

Ratio of tensions:
T1/T2 = (g + a)/(g - a)

Substituting the given values, we get
T1/T2 = (9.8 + 4.9)/(9.8 - 4.9) = 14.7/4.9 = 3/1

Hence, the ratio of tensions is 3:1. Therefore, option (a) is the correct answer.
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