PSC 27 -Questions: Integration in Physics 1

PSC 27 -Questions: Integration in Physics 1

1. The surface charge density of a strip of width W = 0.025 m and length L = 0.150 m is increasing from one end to the other as follows:

where b = 3.00 mC/m⁴. What is the charge on the right half of the strip?

2. The surface charge density of a circular disk of radius R = 0.150 m is changing with the distance from the center as follows:

where a = 5.00 mC/m², b = 1.50 mC/m³. What is the total charge of the circular plate?

3. Find the moments of inertia I_A and I_B of uniform rod of mass M = 1.00 kg and length L = 1.00 m about axes A and B as shown in the figure:

4. The mass density of a centrally symmetric solid sphere of radius R = 0.500 m is given as follows:

where a = 20.0 × 10³ kg/m³ and b = 1.00 × 10³ kg/m⁴ are constants. Find the total mass of the sphere.

5. The mass density of a hollow axially symmetric cylinder of height L = 0.500 m and inner and outer radii R₁ = 0.100 m and R₂ = 0.400 m respectively changes as follows:

where a = 20.0 × 10³ kg/m³ and b = 1.00 × 10³ kg/m are constants.

i.) Find the total mass of the cylinder.

ii.) Find the moment of inertia of the cylinder about its symmetry axis.

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