1
JEE Main 2024 (Online) 29th January Evening Shift
Numerical
+4
-1

A particle is moving in a circle of radius $$50 \mathrm{~cm}$$ in such a way that at any instant the normal and tangential components of it's acceleration are equal. If its speed at $$\mathrm{t}=0$$ is $$4 \mathrm{~m} / \mathrm{s}$$, the time taken to complete the first revolution will be $$\frac{1}{\alpha}\left[1-e^{-2 \pi}\right] \mathrm{s}$$, where $$\alpha=$$ _________.

2
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1
A stone tied to $180 \mathrm{~cm}$ long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $\frac{1936}{x} ms^{-2}$. The value of $x$ ________. (Take $\pi=\frac{22}{7}$ )
3
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1

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 $$t(1-e^{-\pi/2})s$$. The value of t is ____________.

4
JEE Main 2022 (Online) 30th June Morning Shift
Numerical
+4
-1

A person starts his journey from centre 'O' of the park and comes back to the same position following path OPQO as shown in the figure. The radius of path taken by the person is 200 m and he takes 3 min 58 sec to complete his journey. The average speed of the person is _____________ ms$$-$$1. (take $$\pi$$ = 3.14)