Required value of initial speed of the bullet be ( 4M/m)√(gL).
Given parameters:
Mass of the bullet =m.
Mass of the bob of the pendulum = M.
speed of the bullet before collision = v
Speed of the bullet after collision = v/2.
Length of the pendulum stiff rod = L.
Let speed transmitted to the pendulum be u.
Using principle of conservation of momentum:
mv = Mu + mv/2
⇒ Mu = mv/2
⇒ u = (m/M)v/2
We know that: to make the bob over the top of the trajectory without falling backward in its circular path, required speed be = √(4gL). [ where g = acceleration due to gravity]
To be minimum initial speed the bullet must have in order for the pendulum bob to just barely swing through a complete vertical circle:
u = √(4gL)
⇒ (m/M)v/2 = √(4gL)
⇒ v =( 4M/m)√(gL).
Hence, minimum required speed of the bullet be ( 4M/m)√(gL).
Learn more about speed here:
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Basically, the temperature is a result of the average kinetic energy of all the atoms comprising the solid/liquid/gas. In solid, these atoms can just vibrate in place, leaving them to only be able to conduct and radiate heat. However, as you probably know liquids and solids take the shape of their container because the bonds between atoms are loose enough to allow them to freely move around. Due to each individual atom having its own energy, and these atoms being free to move about the liquid/gas they collide with other atoms in the substance. These collisions result in a transfer of energy. Finally, lower energy atoms "sink" and higher energy atoms "rise" thus creating a "convection current".
C. Should be the answer it worked for me