Mass of the stone, m = 0.25 kg
Radius of the circle, r = 1.5 m
Number of revolution per second, n = \(\frac{40}{60}\)= \(\frac{2}{3}\) rps
Angular velocity, \(\omega\) = \(\frac{v}{r}\) =2\(\pi\)𝑛 ………….(i)
The centripetal force for the stone is provided by the tension T, in the string, i.e.,
\(T\) = \(F_{centripetal}\)
= \(\frac{mv^2}{r}\) = mr\(\omega^2\) = \(mr(2\pi n)^2\)
= \(0.25\times 1.5\times \bigg(2\times 3.14\times \frac{2}{3}\bigg)^2\)
= 6.57 N
Maximum tension in the string, \(T_{max}\) = 200 N
\(T_{max}\) = \(\frac{mv^2_{max}}{r}\)
\(\therefore\) \(v_{max}\) = \(\sqrt{\frac{T_{max} \times r}{m}}\)
= \(\sqrt{\frac{200\times 1.5}{0.25}}\)
= \(\sqrt{1200}\)
= 34.64 m/s
Therefore, the maximum speed of the stone is 34.64 m/s.
A sportsman runs around a circular track of radius $ r $ such that he traverses the path ABAB. The distance travelled and displacement, respectively, are:
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.
Find the mean deviation about the median for the data
xi | 15 | 21 | 27 | 30 | 35 |
fi | 3 | 5 | 6 | 7 | 8 |