The breaking strength of a given wire depends on its area of cross section where as the breaking stress is a constant for a given material. Consider the following M.C.Q.:
A cable of length 10m and diameter 2cm can support a maximum load of 800 kg. If the length and the diameter of the cable are reduced to 5m and 1cm respectively, it will be able to support a maximum load of
(a) 200kg (b) 400kg (c) 800kg (d) 1600kg (e)100kg
The breaking strength is independent of the length but is directly proportional to the area of cross section. This follows from the expression for Young’s modulus (Y):
Y = Stress/strain. It is the strain which determines the breaking point of a cable.The strain at the breaking point is a constant for a given material. Since the Young’s modulus is a constant for a given material, the breaking stress also is a constant for a given material. Since the breaking stress is the ratio of the breaking strength to the area of cross section, it follows that the breaking strength is directly proportional to the area of cress section.
In the above problem, the breaking strength of the cable of diameter 2cm is 800 kgwt or(800×g) newton. Since the breaking stress is constant for the material of the cable, we can write, (800×g)/ (π×0.02^2) = mg/(π×0.01^2) where ‘m’ is the load the cable of half the diameter can support. Therefore, m = 200kg [option (a)]. It will be more convenient to write, 800/2^2 = m/1^2 to find ‘m’.
Suppose the breaking stress of a steel cable is ‘s’. What is the breaking stress of a steel cable of double the length and three times the diameter?
The answer, as you know, is ‘s’ since the breaking stress is a constant for a given substance.
Here is a very simple question which may mislead you if you are overconfident:
The Young’s modulus of a piano wire is Y. The Young’s modulus of another piano wire of half the thickness and twice the length is
(a) 2Y (b) 4Y (c) 8Y (d) Y/8 (e) Y
The correct option is (e) since the Young's modulus of a given substance is a constant.
A cable of length 10m and diameter 2cm can support a maximum load of 800 kg. If the length and the diameter of the cable are reduced to 5m and 1cm respectively, it will be able to support a maximum load of
(a) 200kg (b) 400kg (c) 800kg (d) 1600kg (e)100kg
The breaking strength is independent of the length but is directly proportional to the area of cross section. This follows from the expression for Young’s modulus (Y):
Y = Stress/strain. It is the strain which determines the breaking point of a cable.The strain at the breaking point is a constant for a given material. Since the Young’s modulus is a constant for a given material, the breaking stress also is a constant for a given material. Since the breaking stress is the ratio of the breaking strength to the area of cross section, it follows that the breaking strength is directly proportional to the area of cress section.
In the above problem, the breaking strength of the cable of diameter 2cm is 800 kgwt or(800×g) newton. Since the breaking stress is constant for the material of the cable, we can write, (800×g)/ (π×0.02^2) = mg/(π×0.01^2) where ‘m’ is the load the cable of half the diameter can support. Therefore, m = 200kg [option (a)]. It will be more convenient to write, 800/2^2 = m/1^2 to find ‘m’.
Suppose the breaking stress of a steel cable is ‘s’. What is the breaking stress of a steel cable of double the length and three times the diameter?
The answer, as you know, is ‘s’ since the breaking stress is a constant for a given substance.
Here is a very simple question which may mislead you if you are overconfident:
The Young’s modulus of a piano wire is Y. The Young’s modulus of another piano wire of half the thickness and twice the length is
(a) 2Y (b) 4Y (c) 8Y (d) Y/8 (e) Y
The correct option is (e) since the Young's modulus of a given substance is a constant.
You may visit physicsplus.blogspot.com for more multiple choice questions with solution.
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