A clock has $75 \mathrm{~cm}, 60 \mathrm{~cm}$ long second hand and minute hand respectively. In 30 minutes…

A clock has $75 \mathrm{~cm}, 60 \mathrm{~cm}$ long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly (Take $\pi=3.14$ ) :
  1. 140.5
  2. 118.9
  3. 139.4
  4. 220.0

Solution

$\begin{aligned} \mathrm{x}_{\min }= & \pi \times \mathrm{r}_{\min } \\ = & \pi \times \frac{60}{100} \mathrm{~m} . \\ \mathrm{x}_{\text {second }} & =30 \times 2 \pi \times \mathrm{r}_{\text {second }} \\ & =30 \times 2 \pi \times \frac{75}{100} \\ \mathrm{x}= & \mathrm{x}_{\text {second }}-\mathrm{x}_{\min } \\ = & 139.4 \mathrm{~m}\end{aligned}$

Asked in: JEE Main 2024 (08 Apr Shift 1)

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