A particle is rotating in a circular path and at any instant its motion can be described as $\theta=\frac{5 t^{4}}{40}-\frac{t^{3}}{3}$. The angular acceleration of the particle after 10 seconds is ____ $\mathrm{rad} / \mathrm{s}^{2}$.

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Kinematics

A particle is rotating in a circular path and at any instant its motion can be described as

θ = \frac{5 t ^{4}}{40} - \frac{t ^{3}}{3}

. The angular acceleration of the particle after 10 seconds is ____

rad / s^{2}

(A)150
(B)120
(C)130✓ Correct
(D)170

Answer: (C)

Solution

With

θ = \frac{5 t ^{4}}{40} - \frac{t ^{3}}{3} = \frac{t ^{4}}{8} - \frac{t ^{3}}{3}

, the angular velocity is

ω = \frac{d θ}{d t} = \frac{t ^{3}}{2} - t^{2}

and the angular acceleration is

\frac{d ω}{d t} = \frac{3 t ^{2}}{2} - 2 t

. At

t = 10

\frac{3 ( 100 )}{2} - 2 (10) = 150 - 20 = 130 rad/ s^{2}

. The angular acceleration after 10 seconds is

130 rad/ s^{2}

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Kinematics →

More JEE Main questions on Kinematics

A projectile is thrown upward at an angle $6 0^{\circ}$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $4 5^{\circ}$ with the horizontal. The initial speed of the projectile is ______ m/s.
JEE Main 2026View solution →
A river of width 200 m is flowing from west to east with a speed of $18 km / h$ . A boat, moving with speed of $36 km / h$ in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for thi …
JEE Main 2026View solution →
An object is projected with kinetic energy K from a point A at an angle $6 0^{\circ}$ with the horizontal. The ratio of the difference in kinetic energies points B and C to that at point A (see figure), in the absence of air friction is :
JEE Main 2026View solution →
A block is sliding down on an inclined plane of slope $θ$ and at an instant $t = 0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$ . The distance $(S)$ travelled by the block before its velocity become zero, …
JEE Main 2026View solution →
A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with $3 m / s^{2}$ . At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is …
JEE Main 2026View solution →
A bead $P$ sliding on a frictionless semi-circular string $(A C B)$ and it is at point $S$ at $t = 0$ and at this instant the horizontal component of its velocity is $v$ . Another bead $Q$ of the same mass as $P$ is ejected from point $A$ at $t = 0$ …
JEE Main 2026View solution →