Question
Prove that the center of mass of a cone of height $h$ is located at $\left(\frac{h}{4}\right)$ height from its base.
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Answer
self
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A rod of negligible heat cafacity has length $20cm$, area of cross section $1.0cm$ and thermal conductivity $200Wm^{-1^\circ}C^{-1}$. The temperature of one end is maintained at $0^\circ C$ and that of the other end is slowly and linearly varied from $0^\circ C$ to $60^\circ C$ in 10 minutes. Assuming no loss of heat through the sides, find the total heat transmitted through the rod in these $10$ minutes.
→You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘deathwell’ (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25m?
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Figure shows a small body of mass m placed over a larger mass $M$ whose surface is horizontal near the smaller mass and gradually curves to become vertical. The smaller mass is pushed on the longer one at a speed v and the system is left to itself. Assume that all the surfaces are frictionless.
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A laser light bean sent to the moon takes 2.56s to return after reflection at the Moon's surface. Calculate the radius of the lunar orbit around the earth.
A capacitor of capacitance $2.0\mu\text{F}$ is charged to a potential difference of $12V$. It is then connected to an uncharged capacitor of capacitance $4.0\mu\text{F}$ as shown in figure. Find:
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