Question

If in a wrench either the force or the couple of wrenches is zero, then wrench is called
A. null wrench
B. degenerate wrench
C. non-degenerate wrench
D. central wrench

Answer 1

Hint We know that a wrench is the collection of the forces and torques acting on the body. Then we will see R. \[G = 0\] . So, we can get that either couples or the forces are zero. We know that if neither couples nor the force is zero. Then the wrench cannot be degenerated. Here we will get it can be degenerated.

Complete step by step solution
The force and torque vectors that arise in applying Newton's laws to a rigid body can be assembled into a screw called a wrench.
In a rigid body the deformation is zero or negligible. Hence the force or couple cannot deform the body. There can be couples acting on the body which means a pair of equal and opposite forces acting on two different points away from the centre of mass. A wrench is a screw consisting of the torque and the force of the system.
According to the question the force or the couple of wrenches is zero. A degenerate wrench is such a wrench where either the force or the couple is zero.
Hence if in a wrench either the force or the couple of wrenches is zero, then wrench is called degenerate wrench (Option- “B”)

Note If neither of the force or the couple is zero then the wrench is called a non-degenerate wrench. So, option- “C” will not be correct. The dot product is equal to zero. That means the wrench can be degenerated. To get a mathematical formulation for the geometry of the central lines of the rigid body which are the axes of spatial movement and the lines of action of forces, screw theory is used.