
The dimensional formula of effective torsional constant of spring is__________
A)
B)
C)
D)
Answer
515.7k+ views
Hint: We know that in linear motion, friction exists between the two surfaces which is a contact. Similarly, in rotational motion, torsion plays the same role as friction.
Complete step by step solution:
A torsional constant is a physical property of a material. It is mostly used to describe metal beams and is denoted by the variable "C." When a torque is applied to a metal beam, it will twist a certain angle. The angle that the beam twists is dependent on the rigidity, length, and torsional constant. A torsional constant of a beam depends on not only the beam material but also the beam shape.
The torsional constant is a ratio of restoring couples per unit twist.
That is,
Where is the torsion constant of spring
is the deflection in the coil or angle suspended.
is the restoring torque.
Then torsion constant of spring is given by
Apply dimensional formula,
is dimensionless quantity therefore,
The dimensional formula for torsion constant is, . The correct answer is option (C).
Additional information:
The turning effect of a force about an axis of rotation is called torque or moment of force and it is a measure of the rotational effect of the force.
A pair of equal and opposite forces with different lines of action acting on a body is known as a couple. A couple produces rotation without translational motion. For example, our fingers apply a couple to the lid while opening the lid of a bottle. Also, we apply a couple using our fingers to twist wire or thread.
Note:
(i) The torsional constant is a ratio of restoring couples per unit twist.
(ii) In linear motion we have force, and in the case of rotational motion, torque is applied.
Complete step by step solution:
A torsional constant is a physical property of a material. It is mostly used to describe metal beams and is denoted by the variable "C." When a torque is applied to a metal beam, it will twist a certain angle. The angle that the beam twists is dependent on the rigidity, length, and torsional constant. A torsional constant of a beam depends on not only the beam material but also the beam shape.
The torsional constant is a ratio of restoring couples per unit twist.
That is,
Where
Then torsion constant of spring is given by
Apply dimensional formula,
Additional information:
The turning effect of a force about an axis of rotation is called torque or moment of force and it is a measure of the rotational effect of the force.
A pair of equal and opposite forces with different lines of action acting on a body is known as a couple. A couple produces rotation without translational motion. For example, our fingers apply a couple to the lid while opening the lid of a bottle. Also, we apply a couple using our fingers to twist wire or thread.
Note:
(i) The torsional constant is a ratio of restoring couples per unit twist.
(ii) In linear motion we have force, and in the case of rotational motion, torque is applied.
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