A 8.8-kg mass is placed at (2.0, 3.0) m. Where can a 4.4-kg mass be placed so that the moment of inertia about the z axis is zero?Select one:a.(−4.0, −6) mb.(−2.0, −3.0) mc.(−1.0, −1.5) md.​There is no position giving this result.e.(1.0, 1.5) m

The moment of inertia (I) for a point mass is given by the equation I = m*r^2, where m is the mass and r is the distance from the axis of rotation. In this case, we want the total moment of inertia about the z-axis to be zero. This means that the moment of inertia of the 8.8-kg mass must be equal and opposite to the moment of inertia of the 4.4-kg mass.

The 8.8-kg mass is at (2.0, 3.0) m, so its distance from the z-axis (r1) can be calculated using the Pythagorean theorem: r1 = sqrt((2.0)^2 + (3.0)^2) = sqrt(13) m. Therefore, its moment of inertia (I1) is I1 = m1r1^2 = 8.8(sqrt(13))^2 = 114.4 kg*m^2.

We want the moment of inertia of the 4.4-kg mass (I2) to be -114.4 kgm^2, so we can set up the equation I2 = m2r2^2 = -114.4 kg*m^2 and solve for r2. This gives r2 = sqrt(I2/m2) = sqrt(-114.4/4.4) = sqrt(-26) m.

However, the square root of a negative number is not a real number, so there is no real position that the 4.4-kg mass can be placed to give a total moment of inertia of zero about the z-axis. Therefore, the correct answer is d. There is no position giving this result.

The moment of inertia (I) for a point mass is given by the equation I = m*r^2, where m is the mass and r is the distance from the axis of rotation. In this case, we want the total moment of inertia about the z-axis to be zero. This means that the moment of inertia of the 8.8-kg mass must be equal and opposite to the moment of inertia of the 4.4-kg mass.

Let's denote the position of the 4.4-kg mass as (x, y). Then the distance of this mass from the origin is sqrt(x^2 + y^2). The moment of inertia of the 4.4-kg mass is then 4.4sqrt(x^2 + y^2)^2 = 4.4(x^2 + y^2).

The distance of the 8.8-kg mass from the origin is sqrt((2.0)^2 + (3.0)^2) = sqrt(13), so its moment of inertia is 8.8sqrt(13)^2 = 8.813.

Setting these two moments of inertia equal to each other gives us the equation 4.4*(x^2 + y^2) = 8.8*13. Simplifying this equation gives us x^2 + y^2 = 26.

The solutions to this equation are the points on the circle with radius sqrt(26) centered at the origin. However, we want the point that is opposite to the 8.8-kg mass, so we want the point that is a distance of 2*sqrt(26) from the 8.8-kg mass. This point is (-2.0, -3.0), so the correct answer is (b).