A stone tied to the end of a string of 1 m long is whirled in a...

A stone tied to the end of a string of 1

\mathrm{m}

long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?

Options

A $\pi^2 \mathrm{~ms}^{-2}$ and direction along the radius towards the centre
B $\pi^2 \mathrm{~ms}^{-2}$ and direction along the radius away from the centre
C $\pi^2 \mathrm{~ms}^{-2}$ and direction along the tangent to the circle
D $\pi^2 / 4 \mathrm{~ms}^{-2}$ and direction along the radius towards the centre

Correct answer

A. $\pi^2 \mathrm{~ms}^{-2}$ and direction along the radius towards the centre

Step-by-step solution

(a=

\frac{v^2}{r}=\omega^

2 r=4

\pi^

2 n² r=4

\pi^

2\left(\frac{22}{44}\right)^

2

\times

1=

\pi^

2

\mathrm{~m}

/

\mathrm{s}^2) and its direction is always along the radius and towards the centre.

Practice Motion in Two Dimensions on Quantrex Academy →

More from Motion in Two Dimensions

A particle moving with uniform speed in a circular path maintains: NEET 2024 A bob is whirled in a horizontal plane by means of a string with an initial speed of ω… NEET 2024 A particle is executing uniform circular motion with velocity v and acceleration a .… NEET 2023 A ball is projected from point A with velocity 20 ~m ~s^ -1 at an angle 60^ ∘ to the… NEET 2023 A bullet is fired from a gun at the speed of 280m s ^ - 1 in the direction 30 ° above the… NEET 2023 A constant torque of 100 ~N ~m turns a wheel of moment of inertia 300 ~kg ~m^2 about an… NEET 2023 A ball is projected with a velocity, 10 ms ^ - 1 , at an angle of 60 ° with the vertical… NEET 2022 A cricket ball is thrown by a player at a speed of 20 ~m / s in a direction 30^ ∘ above… NEET 2022 Full Motion in Two Dimensions list All NEET PYQs