Question

A uniform metre scale of mass 2kg is suspended from one end .if it's displacement through an angle 60 from vertical the increase in potential energy is

Answer 1

In order to solve this question you must understand few things,

• Since in the question, it was given that the meter ruler is a uniform one. Which means that the mass of the ruler is evenly spread. And the Center of Gravity is acting right at the middle of the ruler.
• When meter ruler lies on the ground (before suspending), We have to take the Potential Energy of the meter ruler is equal to Zero.

Since the total mass of the meter ruler is acting on the Center of gravity, We can take the energy of that point. So on the picture you can see that after suspending, Center of gravity went up from the ground. So if we can find the vertical distance of Center of gravity, we can find the potential energy of the meter ruler,

Sin(60) = X/(0.5)

X = 1/2 x Sin(60)

X = 1/2 x √3/2

  = √3/4

Then,

Potential Energy = mgh

                           = 2 x 10 x √3/4

                           = 5√3 J