Question

A stone tied at the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 25 revolutions in 14 s, what is the magnitude of acceleration of the stone ?

• A. ${90 \,m \, s^{-2}}$
• B. ${100 \,m \, s^{-2}}$
• C. ${110 \,m \, s^{-2}}$
• D. ${120 \,m \, s^{-2}}$

Answer 1

Answer: (B)

${100 \,m \, s^{-2}}$

Answer 2

Length of a string $l$ = 80 cm = 0.8 m
Number of revolutions = 25
Time taken = 14 sec
$\therefore$ Frequency, $\upsilon = \frac{24}{14} = 1.78 \, sec^{-1}$
$\therefore \:\: \omega = 2\pi \upsilon = 2\pi \times{ 1.78 = 11.18 \,rad \,s^{-1}}$
$a = \omega^2 \, l = (11.18)^2 \times { (0.8) = 99.99\, m \, s-2}$
${? 100\, m\, s^{-2}}$