A particle moves along a circle ((20)/(π)) m with constant tangential acceleration. If the velocity of the particle is 80 ~m / s at the end of the second revolution after after motion has begun, the tangential

Correct answer: A. 40 ~m / s^2 From question aligned & r=(20)/(π)m, v=80 ~m/ s & θ=2 revolutions =2 ×2 π=4 π rad & ω^2=ω_0 ^2+2 α θ & ω^2=2 α θ (i) since ω_0=0 & Since α=(a)/(r) and ω= V r aligned Putting these values in eq. (i) aligned & (V^2)/(r^2)= (2 a θ)/(r) & a= (V^2)/(2 r θ)=(80 × 80)/(2 ×((20)/(π)) × 4 π) &=40 ~m/ s^2 aligned

NEET 2003

Exam: NEET
Year: 2003
Subject: Physics
Chapter: Motion in Two Dimensions

NEET 2003 · Physics · Motion in Two Dimensions

A particle moves along a circle ((20)/(π)) m with constant...

A particle moves along a circle

\left(\frac{20}{\pi}\right) \mathrm{m}

with constant tangential acceleration. If the velocity of the particle is

80 \mathrm{~m} / \mathrm{s}

at the end of the second revolution after after motion has begun, the tangential acceleration is:

Options

A $40 \mathrm{~m} / \mathrm{s}^2$
B $640 \pi \mathrm{m} / \mathrm{s}^2$
C $160 \pi \mathrm{m} / \mathrm{s}^2$
D $40 \pi \mathrm{m} / \mathrm{s}^2$

Correct answer

A. $40 \mathrm{~m} / \mathrm{s}^2$

Step-by-step solution

From question

\begin{aligned}& r=\frac{20}{\pi}m, v=80 \mathrm{~m}/ \mathrm{s}\\ & \therefore \theta=2 \text{ revolutions }=2 \times2 \pi=4 \pi \mathrm{rad}\\ & \therefore \omega^2=\omega_0{ }^2+2 \alpha \theta\\ & \therefore \omega^2=2 \alpha \theta \ldots(\mathrm{i}) \text{ since } \omega_0=0 \\ & \text{ Since } \alpha=\frac{a}{r} \text{\text{ and } } \omega=\frac{\mathrm{V}}{r} \end{aligned}

Putting these values in eq. (i)

\begin{aligned}& \frac{V^2}{r^2}= \frac{2 a \theta}{r}\\ & \Rightarrow a= \frac{V^2}{2 r \theta}=\frac{80 \times 80}{2 \times\left(\frac{20}{\pi}\right) \times 4 \pi}\\ &=40 \mathrm{~m}/ \mathrm{s}^2 \end{aligned}

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