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A particle moves along a circle of radius 20π m\frac{20}{\pi} \text{ m} with constant tangential acceleration. If the velocity of the particle is 80 m/s80 \text{ m/s} at the end of the second revolution after motion has begun, the tangential acceleration is:

A

640π m/s2640 \pi \text{ m/s}^2

B

160π m/s2160 \pi \text{ m/s}^2

C

40π m/s240 \pi \text{ m/s}^2

D

40 m/s240 \text{ m/s}^2

Step-by-Step Solution

Let the tangential acceleration of the particle be ata_t. Given: Initial velocity, u=0u = 0 (starts from rest) Final velocity, v=80 m/sv = 80 \text{ m/s} Radius, r=20π mr = \frac{20}{\pi} \text{ m} Number of revolutions, n=2n = 2

The total linear distance ss covered by the particle along the circular path in 2 revolutions is: s=n×2πr=2×2π×(20π)=80 ms = n \times 2\pi r = 2 \times 2\pi \times \left(\frac{20}{\pi}\right) = 80 \text{ m}

Using the third equation of motion (v2=u2+2atsv^2 = u^2 + 2a_ts): (80)2=02+2×at×80(80)^2 = 0^2 + 2 \times a_t \times 80 6400=160at6400 = 160 a_t at=6400160=40 m/s2a_t = \frac{6400}{160} = 40 \text{ m/s}^2.

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