Question

The pendulum bob hinge at O ​​is shown to have the velocity u = u from the bottommost point. If L = 54 cm, find the maximum height (in meters) reached by Bob from the point of projection. 4GL

Answer 1

Answer:

The maximum height (in meters) reached by Bob from the point of projection is 90 cm

Step-by-step explanation:

Given the length = L =  54 cm

At maximum height position, the tension in the string will become zero and at that time string makes an angle of θ

Under that condition,

mgsinθ = mu^2/L - (1)

Now by energy conservation,

$\frac{m(\sqrt{4gL})^{2} }{2} = mg(L+Lsin\theta) + \frac{mu^{2} }{2} \\\\\frac{mu^{2} }{2} = 2gmL-2gmLsin\theta -- (2)$

From equation 1 and 2 we get

sinθ = 2/3

So maximum displacement = L+Lsinθ = 5L/3

maximum displacement = L+Lsinθ = 5L/3 = 5*54/3 = 90 cm