A solid objects is made by removing the to half of a cone of uniform destiny . T

Question

A solid objects is made by removing the to half of a cone of uniform destiny . The remaining bottom half of the cone has a height of H/2, and a base radius of R. Find the distance from the base of the cone to its center of mass expressed in terms of the variables provided. A solid objects is made by removing the to half of a cone of uniform destiny . The remaining bottom half of the cone has a height of H/2, and a base radius of R. Find the distance from the base of the cone to its center of mass expressed in terms of the variables provided.

Explanation / Answer

volume of cone = pir^2h/3
but tan (theta) = r/H
so V = piH^3tan^2(theta)/3

mass of full cone = M
mass of removed cone = M(H/2)^3/H^3 = M/8
mass of leftover part = 7M/8

com of leftover part = y distance from base
com of full cone = H/3 from base
com of removed cone = (H/2 + H/6) = 2H/3 distance from the base [ because com of a cone is H/3 from the base]

hence, MH/3 = M*2H/24 + 7M*y/8
H/3 - H/12 = 7y/8
H = 7y/2
y = 2H/7 distacne from the base

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.