Oscillations

JEE Main level, single correct, medium

173 of 194

Question 173 of 194

In an experiment to determine the period of a simple pendulum of length 1m1m, it is attached to different spherical bobs of radii r1{r}_{1} and r2{r}_{2} . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10−4s5\times {10}^{-4}s, the difference in radii, ∣r1−r2∣\left|{r}_{1}-{r}_{2}\right| is best-given by

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Answer: (B) 0.05cm0.05cm

T=2πlgT=2\pi \sqrt{\dfrac{l}{g}}

T∝lT\propto \sqrt{l}

l=1l=1

ΔTT=12Δll\dfrac{\Delta T}{T}=\dfrac{1}{2}\dfrac{\Delta l}{l}

Δl=r1−r2\Delta l={r}_{1}-{r}_{2}⇒∆l=2∆TT×l\Rightarrow ∆l=\dfrac{2∆T}{T}\times l

=2×5×10−42×1m=\dfrac{2\times 5\times {10}^{-4}}{2}\times 1m

=5×10−2cm= 5\times {10}^{-2}\text{cm}

=0.05cm=0.05cm

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