Question

The pendulum bob has a speed of 3 ms^-1 at its lowest position and the length of the pendulum is 0.5 m. The speed of the bob when the length of the pendulum makes an angle of 60° with the vertical will be ______.

Options

• 1.5 ms^-1

• 2 ms^-2

• 2.7 ms^-1

• 3.2 ms^-2

Answer 1

The pendulum bob has a speed of 3 ms^-1 at its lowest position and the length of the pendulum is 0.5 m. The speed of the bob when the length of the pendulum makes an angle of 60° with the vertical will be 2 ms^-2.

Explanation:

Given, l = 0.5 m, u = 3 ms^-1

The situation is shown below.

Applying energy conservation at points A and B,

`1/2m u^2 = 1/2m"v"^2 + mgh`

⇒ u² = v² + 2gh

v² = u² - 2gh = u² - 2g(l - l cos60°)

[since, h = MA = OA - OM = l - OB cos60° = l - l cos60°]

= `(3)^2 - 2(9.8)(0.5 - 0.5 xx 1/2)`

⇒ v² = 4

∴ v = 2 ms^-1