# Lesson Worksheet: The Negative Mass Method Mathematics

In this worksheet, we will practice finding the center of gravity of a lamina that contains holes using the negative mass method.

Q1:

The table shows the distribution of a system of masses on a uniform lamina.

Mass of the Lamina Mass Added Mass Removed

Which of the following is the center of mass of this system?

• A
• B
• C
• D
• E

Q2:

A uniform lamina of mass 15 kg has its center of mass at . If a piece of the lamina is cut out whose mass is 11 kg and whose center of mass is at , find the coordinates of the center of mass of the remaining part.

• A
• B
• C
• D
• E

Q3:

An equilateral triangle has a side length of 82 cm. When three equal masses are placed at the vertices of the triangle, the centre of mass of the system is . When the mass at vertex is removed, the centre of mass of the system is . Find the coordinates of the centre of mass of the two systems and . • A,
• B,
• C,
• D,

Q4:

Find the coordinates of the center of gravity of the following figure, which is drawn on a grid of unit squares. • A
• B
• C
• D
• E

Q5:

A square-shaped uniform lamina has a side length of 28 cm. A circular disk of radius 7 cm was cut out of the lamina such that its center was at a distance of 17 cm from both and . Determine the coordinates of the center of mass of the resulting lamina. Take . • A
• B
• C
• D

Q6:

The diagram shows a uniform lamina from which a triangle has been cut out. was an equilateral triangle with a side length of 93 cm and center of mass . Find the coordinates of the new center of mass of the resulting lamina. Round your answer to two decimal places if necessary. • A
• B
• C
• D

Q7:

The figure shows a uniform circular lamina of radius 5.6 cm and centre . A circular disc of radius 2.4 cm and centre has been removed from the lamina as shown. Determine the distance in centimetres between and the centre of mass of the resulting lamina.

• A cm
• B cm
• C cm
• D cm

Q8:

A uniform lamina is in the form of a rectangle , where and . Two points and are on such that . The triangle , where is the center of the rectangle, is cut out of the lamina. Find the coordinates of the center of mass of the resulting lamina. Given that the lamina was freely suspended from , find the tangent of the angle that makes to the vertical, , when the lamina is hanging in its equilibrium position. • A,
• B,
• C,
• D,

Q9:

The figure shows a uniform square lamina of side length 18 cm. It is divided into nine congruent squares as shown. Given that the square was cut out and stuck onto square , determine the coordinates of the center of gravity of the resulting lamina. • A
• B
• C
• D

Q10:

A uniform square-shaped lamina of side length 222 cm has a mass of one kilogram. The midpoints of , , and are denoted by , , and respectively. The corners and were folded over so that they lie flat on the surface of the lamina. Bodies of masses 365 g and 294 g were attached to the points and respectively. Find the coordinates of the center of mass of the system rounding your answer to two decimal places if necessary. • A
• B
• C
• D

This lesson includes 35 additional questions and 258 additional question variations for subscribers.