Three forces acting on a rigid body are represented in magnitude, direction and line of action by the three sides of a triangle taken in order. The forces are equivalent to a couple whose moment is equal to
- A.Thrice the area of the triangle
- B.Twice the area of the triangle
- C.The area of the triangle
- D.Half the area of the triangle
Correct answer
Explanation
The correct answer is B, twice the area of the triangle. When three forces are represented by the sides of a triangle taken in order, their vector sum is zero, because the three sides close the triangle, so the body cannot be pushed away; but the lines of action are different, so the system reduces to a couple. Taking moments about any vertex, only the opposite side contributes, and that moment equals the side multiplied by the perpendicular distance from the vertex, which is twice the area of the triangle since the area is half the base into the height. The result is a standard theorem of mechanics and is independent of the point about which moments are taken, as it must be for a couple. Options A, C and D are wrong because they give the wrong multiple of the area; only twice the area follows from the base into height relation.
Read the full article: Centre of Gravity, Torque and Equilibrium: Exam Notes
Practice Questions
View allWhat is the SI unit of torque?
- A.Newton
- B.Newton metre
- C.Newton per metre
- D.Joule per second
Show answer
Torque is the product of a force and the perpendicular distance of its line of action from the axis of rotation, so its unit is the unit of force multiplied by the unit of length, the newton metre, and its dimensional formula is M L squared T to the power…
Read the full explanation →The centre of gravity of a uniform circular ring lies
- A.On the ring itself, at any point
- B.At the centre of the ring, outside its material
- C.At one third of the radius from the centre
- D.Nowhere, because a ring has no centre of gravity
Show answer
The centre of gravity is a geometrical point through which the resultant weight of a body acts, and by symmetry that point for a uniform ring is its geometrical centre, which lies in the empty space inside the ring.
Read the full explanation →The torque produced by a force about an axis is maximum when the angle between the force and the arm is
- A.0 degree
- B.45 degrees
- C.90 degrees
- D.180 degrees
Show answer
The magnitude of torque is r into F into the sine of the angle between the arm and the force, and the sine of an angle is largest, equal to one, at 90 degrees, so the whole of the force is then used in turning the body.
Read the full explanation →A long spanner loosens a tight nut more easily than a short one because it
- A.Reduces the force needed by increasing the moment arm
- B.Reduces the friction at the nut
- C.Increases the mass acting on the nut
- D.Changes the direction of the weight of the nut
Show answer
Torque is the product of the force and the perpendicular distance of its line of action from the axis, so the same turning effect can be produced by a smaller force if that distance is made larger; a long handle therefore does the same work with less effort.
Read the full explanation →A rigid body is said to be in complete mechanical equilibrium when
- A.The net force on it is zero
- B.The net torque on it is zero
- C.Both the net force and the net torque on it are zero
- D.Its centre of gravity lies at its geometrical centre
Show answer
A zero net force gives translational equilibrium, so the body as a whole does not accelerate, and a zero net torque gives rotational equilibrium, so it does not begin to spin; complete equilibrium requires the two together.
Read the full explanation →