Question

· A simple pendulum of length 100 cm
performs S.H.M. Find the restoring force
acting on its bob of mass 50 g when the
displacement from the mean position is 3 cm.​

Answer 1

$\dag \: \underline{\sf AnsWer :}$

• We are provided a simple pendulum whose length of string (l) is 100 cm. convert the unit of length of string from cm to m then we get length as 1 m. we are also given the mass of simple pendulum (m) = 50 g = 5 × 10⁻³ kg and displacement (x) = 3 cm = 3 × 10⁻² m. We need to find the restoring force (F) acting on the bob. So, let's solve :

$:\implies\sf \omega =\sqrt{ \dfrac{K}{m}}$

$:\implies\sf \omega^{2} =\dfrac{K}{m}$

$:\implies\sf K = m\omega^{2}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━

$\qquad \: \bigstar \: \underline{\textbf{Finding Angular velocity :}}$

$:\implies\sf T =2\pi \sqrt{\dfrac{L}{g}}$

$:\implies\sf \dfrac{2\pi}{ \omega} =2\pi \sqrt{\dfrac{L}{g}}$

$:\implies\sf \dfrac{1}{ \omega} =\sqrt{\dfrac{L}{g}}$

$:\implies\sf \omega =\sqrt{\dfrac{g}{L}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━

$\qquad \: \bigstar \: \underline{\textbf{Finding Restoring force :}}$

$\dashrightarrow\:\:\sf F = -kx$

$\dashrightarrow\:\:\sf F = -(m \omega^{2} )x$

$\dashrightarrow\:\:\sf F = -m \times \Bigg(\sqrt{\dfrac{g}{L}}\Bigg)^{2} \times x$

$\dashrightarrow\:\:\sf F = -m \times \dfrac{g}{L}\times x$

$\dashrightarrow\:\:\sf F = -50 \times 10^{ - 3} \times \dfrac{10}{1}\times 3 \times {10}^{ - 2}$

$\dashrightarrow\:\:\sf F = -1500 \times 10^{ - 5}$

$\dashrightarrow\:\: \underline{ \boxed{\sf F = -1.5 \times 10^{ - 2} \: N }}$