In anelectricclockthe extremityof thehourhandmovesonetwentiechas fastas thatof theminutehand. Whatis thelengthof thehourif the minutehandis 10cm long ?

In anelectricclockthe extremityof thehourhandmovesonetwentiechas fasta

1.	In anelectricclockthe extremityof thehourhandmovesonetwentiechas fastas thatof theminutehand. Whatis thelengthof thehourif the minutehandis 10cm long ?
Answer» Solution :The angular speed of the HOUR hand ,`omega^(H) = (2pi)/(3600 xx 12)` rad /SEC The angular speed of the minute hand , `omega_(M) = (2pi)/(3600)` rad/sec . LET `r_(H)` be the length of the hour hand . `therefore` The LINEAR speed of the extremity of the hour hand is given by V = `r omega` `therefore v _(H) = r_(H) omega_(H)` Similary , for the minute hand , `V_(M) = r_(M) omega_(M)` Now , by problem , `v_(H) = (1)/(20) v_(M) or r_(H) omega_(H) = (1)/(20) r_(M) omega_(M)` `therefore r_(H) xx (2pi)/(3600 xx 12) = (1)/(20) xx 10 xx (2pi)/(3600) or r_(H) = 6` cm