The correct answer to the question is : (A) 245 J and (B) 7.92 m/s
EXPLANATION :
As per the question, the mass of the bead m = 5.0 Kg.
The height of the point A from the ground h = 5 m.
First we are asked to calculate the energy of the bead at point A.
The energy possessed by the bead at the point A is the gravitational potential energy.
Hence, the gravitational potential energy of the bead at the point A is calculated as -
Potential energy P.E = mgh
= 5 × 9.8 × 5 joule
= 245 J. [ANS]
Now we are asked to calculate the velocity at point C.
The potential energy of the bead at point B is equal to the kinetic energy of the bead at point C . It is so because the potential energy of the bead gradually converts into into kinetic energy when the bead comes from point B to point C.
Hence, potential energy at B = Kinetic energy at C.
⇒ mgh = [tex]\frac{1}{2}mv^2[/tex]
⇒ 2gh = [tex]v^2[/tex]
⇒ v = [tex]\sqrt{2gh}[/tex]
= [tex]\sqrt{2\times9.8\times 3.20}\ m/s[/tex]
= 7.92 m/s. [ans]
