The metallic bob of simple pendulum has the relative density. 5 The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes <math> <mrow> <mn>5</mn> <mroot> <mrow> <mi>x</mi> </mrow> <mrow></mrow> </mroot> <mtext> </mtext> <mi>s</mi> <mo>.</mo> </mrow> </math> The value of x will be_______.

geff = g – <!- [if gte mso 9]><xml> </xml><! [endif]-> ( ρ w ρ b ) g T = 2 π l g T ' = 2 π l g e f f ⇒ T ' = 5 4 T = <!- [if gte mso 9]><xml> </xml><! [endif]-> 5 4 × 1 0 = <!- [if gte mso 9]><xml> </xml><! [endif]-> 5 5 s e c So, x = 5

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Physics Class 11th Physics Oscillations

The metallic bob of simple pendulum has the relative density. 5 The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes $5 \sqrt[]{x} s .$ The value of x will be_______.

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alok kumar singh | Contributor-Level 10

2 months ago

g_eff = g – $(\frac{ρ_{w}}{ρ_{b}}) g$

$T = 2 π \sqrt[]{\frac{l}{g}}$

$T' = 2 π \sqrt[]{\frac{l}{g_{e f f}}}$

$\Rightarrow T' = \sqrt[]{\frac{5}{4}} T$

= $\sqrt[]{\frac{5}{4}} \times 10$

= $5 \sqrt[]{5} s e c$

So, x = 5

geff = g – <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1815209329"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mrow> <mo> (</mo> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>ρ</mi> </mrow> <mrow> <mi>w</mi> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>ρ</mi> </mrow> <mrow> <mi>b</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>g</mi> </mrow> </math> <math> <mrow> <mi>T</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mi mathvariant="script">l</mi> </mrow> <mrow> <mi>g</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <mi>T</mi> <mo>'</mo> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mi mathvariant="script">l</mi> </mrow> <mrow> <msub> <mrow> <mi>g</mi> </mrow> <mrow> <mi>e</mi> <mi>f</mi> <mi>f</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <mo>⇒</mo> <mi>T</mi> <mo>'</mo> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> <mi>T</mi> </mrow> </math> = <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1815209333"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mroot> <mrow> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> <mo>×</mo> <mn>1</mn> <mn>0</mn> </mrow> </math> = <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1030" DrawAspect="Content" ObjectID="_1815209334"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mn>5</mn> <mroot> <mrow> <mn>5</mn> </mrow> <mrow></mrow> </mroot> <mi>s</mi> <mi>e</mi> <mi>c</mi> </mrow> </math> So, x = 5

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The metallic bob of simple pendulum has the relative density. 5 The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes $5 \sqrt[]{x} s .$ The value of x will be_______.

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The metallic bob of simple pendulum has the relative density. 5 The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes 5 x s . The value of x will be_______.

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The metallic bob of simple pendulum has the relative density. 5 The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes $5 \sqrt[]{x} s .$ The value of x will be_______.