Question

A pendulum is swinging in a semi circular path
and the maximum speed of the bob at the lowest
position is 7m/s. If g = 9.8 m/s2, then length of
the pendulum is
(a) 1 m
(b) 2.5 m
(c) 1.5 m
(d) 2.0 m​

Answer 1

Answer:

Apply energy conservation theorem,

energy at lowest position of Bob = energy , when Bob makes 60° to the vertical

1/2 mv² = 1/2 mv₁² + mgl(1 - cos60°)

Here v is speed at Lowest position , v₁ is speed , when it makes 60° with vertical and l is length of pendulum .

[Actually, height of Bob , when it makes 60° with vertical = l(1 - cos60°)]

∴ v² = v₁² + 2gl(1 - cos60°)

3² = v₁² + 2 × 10 × 0.5 (1 - 1/2)

9 = v₁² + 5

v₁² = 4 ⇒v₁ = 2m/s

Hence, speed of Bob = 2m/s

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Explanation:

Answer 2

Answer:

Explanation:

If path is semicircular, amplitude is πl/2.

Where l is length of the pendulum