A clock has 75 cm and 60 cm long second han | vedclass

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(C) The length of the second hand is $r_s = 75 \ cm = 0.75 \ m$. The length of the minute hand is $r_m = 60 \ cm = 0.60 \ m$.In $30$ minutes,the secon

Vedclass · Accepted Answer

$139.4$

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(C) The length of the second hand is $r_s = 75 \ cm = 0.75 \ m$. The length of the minute hand is $r_m = 60 \ cm = 0.60 \ m$.In $30$ minutes,the second hand completes $30$ full revolutions. The distance traveled by the tip of the second hand is $d_s = 30 	imes (2 \pi r_s) = 30 	imes 2 	imes 3.14 	imes 0.75 = 141.3 \ m$.In $30$ minutes,the minute hand completes $0.5$ revolutions (half a circle). The distance traveled by the tip of the minute hand is $d_m = 0.5 	imes (2 \pi r_m) = \pi r_m = 3.14 	imes 0.60 = 1.884 \ m$.The difference in distance is $x = d_s - d_m = 141.3 - 1.884 = 139.416 \ m$.Rounding to one decimal place,$x \approx 139.4 \ m$.

$A$ clock has $75 \ cm$ and $60 \ cm$ long second hand and minute hand respectively. In $30$ minutes duration,the tip of the second hand will travel $x$ distance more than the tip of the minute hand. The value of $x$ in meters is nearly (Take $\pi = 3.14$):

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