A simple pendulum of time period 1s and length l is hung from a fixed support at O, such that the bob is at a distance H vertically above A on the ground (Fig) The amplitude is θ o . The string snaps at θ = θ₀ /2. Find the time taken by the bob to hit the ground. Also find distance from A where bob hits the ground. Assume θ₀ to be small so that sin _o ₀ and cos ₀

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Payal Gupta | Contributor-Level 10

7 months ago

This is a long answer type question as classified in NCERT Exemplar

Let us assume t=0 when $θ = θ$ _o then $θ$ = $θ$ ₀coswt

Given a seconds pendulum w=2 $π$

$θ$ = $θ_{o} c o s 2 π t$

At time t, let $θ = θ_{o} / 2$

Cos2 $π t_{1} = \frac{1}{2}$ , t₁=1/6

$\frac{d θ}{d t}$ =-( $θ_{o} 2 π$ )sin2 $π t$

t=t₁=1/6

d $\frac{θ}{d t}$ =- $θ_{o} 2 π$ sin $\frac{2 π}{6} = - \sqrt[]{3} π θ_{o}$

the linear velocity is u=- $\sqrt[]{3} π θ_{o} l$

the vertical component is U_y= $- \sqrt[]{3} π l s i n (\frac{θ_{o}}{2})$

the horizontal component U

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Physics NCERT Exemplar Solutions Class 11th Chapter Fourteen 2025

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