Physics, asked by sreeshmapsreenivas, 2 months ago

2. A stone tied to the end of a string is whirled in a circular path of radius 50 cm with a constant speed. If the stone makes 200 revolutions in 5 minutes, find the linear speed of the ston


Answers

Answered by RISH4BH
11

GiveN :-

  • A stone tied to the end of a string is whirled in a circular path of radius 50 cm with a constant speed.
  • The stone makes 200 revolutions in 5 minutes .

To FinD :-

  • The linear speed of the stone .

SolutioN :-

Given that. , a stone is tied with a string of lenght 50cm .It makes 200 revolutions in a minute . We need to find the linear speed of the stone . First of all we know that liner speed is equal to product of angular velocity and radius . That is , \sf v = r \omega .So we need to Find the angular velocity is \sf 2\pi n .

\red{\frak{We \ Know  }}\begin{cases} \textsf{ Angular velocity as } \bf\omega \\\textsf{ Frequency as \textbf{ n}} . \\\textsf{ Linear Speed as \textbf{v}}.\\\textsf{ Radius as \textbf{r}}. \end{cases}

Using the formula :-

\sf\dashrightarrow \pink{ v = r \omega }\\\\\sf\dashrightarrow  v = r \times ( 2 \pi n ) \\\\\sf\dashrightarrow  v = 2 \times \dfrac{50m}{100} \times \dfrac{22}{7}\times \dfrac{200}{5\times 60s} \\\\\sf\dashrightarrow  v = \dfrac{1}{2}\times 2 \times 3.14 \times \dfrac{200}{300} m/s \\\\\sf\dashrightarrow  v = 3.14 \times \frac{2}{3} \\\\\sf\dashrightarrow  \underset{\blue{\sf Required \ speed}}{\underbrace{\boxed{\pink{\frak{ Linear \ speed = 2.09 \ m/s }}}}}

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