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
Correct answer
Explanation
The correct answer is C, both the net force and the net torque on it are zero. 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. Option A is insufficient, and the couple is the standard counter example: two equal and opposite parallel forces with different lines of action add up to zero force, yet the body rotates. Option B is also insufficient, since the torques about an axis may cancel while an unbalanced force still carries the body away in a straight line. Option D is irrelevant: the position of the centre of gravity decides how stable a body is once it is in equilibrium, not whether it is in equilibrium at all.
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
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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 →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
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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.
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
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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
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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
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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.
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