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Question: A string tied on a roof can bear a maximum tension of \(50kgwt\). The minimum acceleration that can ...

A string tied on a roof can bear a maximum tension of 50kgwt50kgwt. The minimum acceleration that can be acquired by a man of 98kg to descend will be: (Take g=9.8m/s2g = 9.8m/{s^2})
A. 9.8m/s29.8m/{s^2}
B. 4.9m/s24.9m/{s^2}
C. 4.8m/s24.8m/{s^2}
D. 5m/s25m/{s^2}

Explanation

Solution

It is the Weight of a man which gives acceleration to him. But as the man is descending, the tension opposes the weight. The tension (T) will be T=mg−maT = mg - ma, where m is the mass of the person, g is the gravity and a is the acceleration acquired by the man. Substitute the values of tension, mass and gravity to calculate the value of acceleration acquired by the man to descend.

Complete step by step answer:
We are given that a string tied on a roof can bear a maximum tension of 50kgwt50kgwt and the mass of a man is 98kg.
We have to calculate the acceleration that can be acquired by him to descend the roof.
Tension (T) on an object or a body is equal to T=mg−maT = mg - ma, where mass, gravity and the tension are given and we need to calculate the value of ‘a’.
T=mg−maT = mg - ma
Send ‘T’ to the right hand side and the term ‘ma’ to the left hand side.
ma=mg−T a=mg−Tm  ma = mg - T \\\ a = \dfrac{{mg - T}}{m} \\\
Expand the division.
a=mgm−Tm   ⟹  a=g−Tm  a = \dfrac{{mg}}{m} - \dfrac{T}{m} \\\ \implies a = g - \dfrac{T}{m} \\\
Substitute the values of tension, gravity and the mass in the above expression to calculate the acceleration.
Tension is given as 50kgwt.
Tension is given in terms of weight (wt), weight is the product of mass and gravity, so multiply the value of gravity to it.
T=50kgwt   ⟹  T=50×9.8kg a=g−Tm g=9.8m/s2,m=98kg,T=50×9.8kg a=9.8−50×9.898=9.8−49098   ⟹  a=9.8−5 ∴a=4.8m/s2  T = 50kgwt \\\ \implies T = 50 \times 9.8kg \\\ a = g - \dfrac{T}{m} \\\ g = 9.8m/{s^2},m = 98kg,T = 50 \times 9.8kg \\\ a = 9.8 - \dfrac{{50 \times 9.8}}{{98}} = 9.8 - \dfrac{{490}}{{98}} \\\ \implies a = 9.8 - 5 \\\ \therefore a = 4.8m/{s^2} \\\
Therefore, the acceleration that can be acquired by the man to descend will be 4.8m/s24.8m/{s^2}

So, the correct answer is “Option C”.

Note:
Tension is the force which acts on a body when it is hung from other objects like rope, roof, chain etc. Acceleration due to gravity is a constant (9.8 or 10) and it is the acceleration acquired by a body due to the gravitational force; whereas acceleration of an object is the rate at which the object changes its velocity and this can vary from person to person or object to object. Acceleration due to gravity and normal acceleration are not the same. At times they both are the same under certain conditions.