If a simple pendulum of length l has maximum angular displacement θ, then the maximum kinetic energy of bob of mass m is

Question

If a simple pendulum of length l has maximum angular displacement θ, then the maximum kinetic energy of bob of mass m is (A) (1/2) ×((l/g)) (B) (1/2)× (mg /l) (C) m g l ×(1- cos θ) (D) (1/2) × m g l sin θ

Tardigrade Admin · Accepted Answer

From the figure, A C=l cos θ <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/2e2be5979e757536495ccc4f34ce0f53-.png" /> ∴ O C=O A-A C =l-l cos θ=l(1- cos θ) Maximum KE of bob at O= Maximum PE of bob at B = ma × O C=m g l(1- cos θ)

Q. If a simple pendulum of length $l$ has maximum angular displacement $θ$ , then the maximum kinetic energy of bob of mass $m$ is

$\frac{1}{2} \times (\frac{l}{g})$

$\frac{1}{2} \times \frac{m g}{l}$

$m g l \times (1 - cos θ)$

$\frac{1}{2} \times m g l sin θ$

From the figure, $A C = l cos θ$

$∴ OC = O A - A C$
$= l - l cos θ = l (1 - cos θ)$
Maximum $K E$ of bob at $O =$ Maximum $PE$ of bob at $B$
$= ma \times OC = m g l (1 - cos θ)$

Q. If a simple pendulum of length l has maximum angular displacement θ, then the maximum kinetic energy of bob of mass m is

21​×(gl​)

21​×lmg​

mgl×(1−cosθ)

21​×mglsinθ