A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200g. The bob is pulled aside until the string is at 60° with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be_________ ms^-1. (if g = 10m/s²)

 

 

From conservation of Energy:

$mg\mathcal{l}\left(1-cos60°\right)=\frac{1}{2}m{v}^2$

$\Rightarrow v^2=2g\mathcal{l}\left(\frac{1}{2}\right)=g\mathcal{l}$

$=10\times \frac{25}{10}=5m/s$

<p>From conservation of Energy:</p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1757930958phpkS8T6y.jpeg" alt="" width="116" height="99" loading="lazy"></picture></div></div><p><span contenteditable="false"> <math> <mrow> <mi>m</mi> <mi>g</mi> <mi mathvariant="script">l</mi> <mrow> <mo> (</mo> <mrow> <mn>1</mn> <mo>−</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>6</mn> <mn>0</mn> <mo>°</mo> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>m</mi> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mi>g</mi> <mi mathvariant="script">l</mi> <mrow> <mo> (</mo> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>g</mi> <mi mathvariant="script">l</mi> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mo>=</mo> <mn>1</mn> <mn>0</mn> <mo>×</mo> <mfrac> <mrow> <mn>2</mn> <mn>5</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> </mrow> </mfrac> <mo>=</mo> <mn>5</mn> <mi>m</mi> <mo>/</mo> <mi>s</mi> </mrow> </math> </span></p>

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