Student Login

Home›Chapters›Circular Motion PYQs›Non-Uniform Circular Motion›Question 14

JEE Main 2023 (29 Jan, Shift 2) · Non-Uniform Circular Motion

Non-Uniform Circular Motion question from JEE Main 2023 (29 Jan, Shift 2)

Q14JEE Main 2023 · 29 JAN · SHIFT 2Difficult

Non-Uniform Circular Motion

A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54 km/hr is $t(1 - e^{-\pi/2})\text{ s}$ . The value of t is ____________.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 40

$a_t = a_c$ : $\frac{dv}{dt} = \frac{v^2}{R}$ gives $s = -R\ln\left(1 - \frac{v_0 t}{R}\right)$
Quarter revolution, $s = \frac{\pi R}{2}$ : $t = \frac{R}{v_0}\left(1 - e^{-\pi/2}\right)$
$v_0 = 54$ km/h $= 15$ m/s, $\frac{R}{v_0} = \frac{600}{15} = 40$
So $t = 40$ s

Report a mistake

More questions on Non-Uniform Circular Motion

A particle of mass m is moving in a circular path of constant radius r such that its…JEE Main 2022 (28 Jun, Shift 1)
A particle at rest starts moving with a constant angular acceleration of 4 rad/s² in a…MHT CET 2021 (20 Sep, Shift 2)
A body is moving along a circular track of radius 100 m with velocity 20 m/s. Its…MHT CET 2020 (19 Oct, Shift 2)
In non-uniform circular motion, the ratio of tangential to radial acceleration is ( r =…MHT CET 2020 (16 Oct, Shift 1)
A particle starting from rest moves along the circumference of a circle of radius r with…MHT CET 2020 (16 Oct, Shift 2)
A child starts running from rest along a circular track of radius r with constant…MHT CET 2020 (19 Oct, Shift 2)
A point P moves in counter-clockwise direction on a circular path as shown in the figure…JEE Main 2010 (AIEEE)
A car is travelling at 40 m/s on a circular path of radius 40 m. It is increasing its…MHT CET 2026 (20 Apr, Shift 2)