Rotational Motion

26 JEE Main questions · Physics

Rotational dynamics

PhysicsJEE Main 21 Jan 2026, Shift 1·Q14·MCQ·Moderate
Open
A uniform rod of mass $m$ and length $l$ is suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is . ( $g$ acceleration due to gravity)
1. (1) $mg/2$
2. (2) $mg/4$
3. (3) $mg/3$
4. (4) $mg$
We corrected a printing error in the original paper
Source printed “length $l$ suspended by means of”.
PhysicsJEE Main 21 Jan 2026, Shift 2·Q7·MCQ·Moderate
Open
The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M. Two blocks of mass of M and m are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in vertical plane about its centre. The magnitude of the acceleration experienced by the blocks is (assume no slipping of string on pulley.)
1. (1) $\dfrac{(M-m)g}{\left[\left(\dfrac{13}{6}\right)M + m\right]}$
2. (2) $\dfrac{(M-m)g}{M + m}$
3. (3) $\dfrac{(M-m)g}{\left[\left(\dfrac{8}{3}\right)M + m\right]}$
4. (4) $\dfrac{(M-m)g}{2M + m}$
We corrected a printing error in the original paper
Source printed “The magnitudes of the acceleration … is”.
PhysicsJEE Main 22 Jan 2026, Shift 2·Q22·Numerical·Moderate
Open
Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius $r = 0.1$ m. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended through a height of 3.6 m is m/s. (Assume string does not slip and $g = 10\ \mathrm{m/s^2}$ )
PhysicsJEE Main 23 Jan 2026, Shift 1·Q17·MCQ·Easy–moderate
Open
Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is:
1. (1) $\dfrac32\dfrac{L}{md^2}$
2. (2) $\dfrac{2L}{md^2}$
3. (3) $\dfrac43\dfrac{L}{md^2}$
4. (4) $\dfrac{2L}{5md^2}$
PhysicsJEE Main 24 Jan 2026, Shift 1·Q16·MCQ·Moderate
Open
Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is $\mathrm{kg.m^2}$ .
( $g = 9.8\ \mathrm{m/s^2}$ )
1. (1) $9.5\times10^{-3}$
2. (2) $4.75\times10^{-3}$
3. (3) $1.86\times10^{-2}$
4. (4) $8.3\times10^{-3}$
PhysicsJEE Main 24 Jan 2026, Shift 2·Q6·MCQ·Moderate
Open
A thin uniform rod (X) of mass $M$ and length $L$ is pivoted at a height $\left(\dfrac{L}{3}\right)$ as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top, is . ( $g$ = gravitational acceleration)
1. (1) $\sqrt{\dfrac32\dfrac{g}{L}}$
2. (2) $\dfrac{3}{\sqrt2}\sqrt{\dfrac{g}{L}}$
3. (3) $\dfrac{1}{\sqrt2}\sqrt{\dfrac{g}{L}}$
4. (4) $\sqrt{\dfrac{3g}{L}}$
PhysicsJEE Main 28 Jan 2026, Shift 1·Q4·MCQ·Moderate
Open
Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure.
If the mass of each disc is 600 gm and applied torque between two discs is $43\times10^{5}$ dyne cm, the angular acceleration of the discs about the given axis $AB$ is $\mathrm{rad/s^2}$ .
1. (1)22
2. (2)11
3. (3)100
4. (4)27
PhysicsJEE Main 28 Jan 2026, Shift 2·Q25·Numerical·Moderate
Open
A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to a 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is J. ( $g = 10\ \mathrm{m/s^2}$ ; take the fly wheel as a uniform disc)
We corrected a printing error in the original paper
Assumption “take the fly wheel as a uniform disc” added; the source leaves the shape unstated (a ring would give 45 J).
PhysicsJEE Main 5 Apr 2026, Shift 2·Q6·MCQ·Easy–moderate
Open
An object of uniform density rolls up the curved path with the initial velocity $v_0$ as shown in the figure. If the maximum height attained by an object is $\dfrac{7v_0^2}{10g}$ ( $g$ = acceleration due to gravity), the object is a.
1. (1)solid cylinder
2. (2)ring
3. (3)disc
4. (4)solid sphere
PhysicsJEE Main 6 Apr 2026, Shift 1·Q6·MCQ·Moderate
Open
A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are and respectively.
1. (1) $0.128\,\pi$ Nm, 100
2. (2) $0.0128\,\pi$ Nm, 50
3. (3) $0.128\,\pi$ Nm, 50
4. (4) $0.0128\,\pi$ Nm, 100
PhysicsJEE Main 6 Apr 2026, Shift 2·Q3·MCQ·Moderate
Open
A solid sphere (A) of mass, $5m$ and spherical shell (B) of mass $m$ , both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B, they start rolling without slipping with an acceleration of $a_A$ and $a_B$ , respectively. The ratio of $a_A$ and $a_B$ is .
1. (1) $5 : 21$
2. (2) $6 : 10$
3. (3) $21 : 25$
4. (4) $1 : 5$
PhysicsJEE Main 8 Apr 2026, Shift 2·Q7·MCQ·Moderate
Open
A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t = 0$ the cylinder has a translational velocity $v_0 = 49$ m/s, perpendicular to its axis and a rotational velocity $v_0/4R$ about the centre. The time taken by the cylinder to start rolling is seconds. (coefficient of kinetic friction $\mu_K = 0.25$ and $g = 9.8\ \mathrm{m/s^2}$ )
1. (1)15
2. (2)5
3. (3)10
4. (4)7.5

Moment of inertia

PhysicsJEE Main 21 Jan 2026, Shift 1·Q23·Numerical·Easy–moderate
Open
Two identical thin rods of mass $M$ kg and length $L$ m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is $\dfrac{x}{12}ML^2\ \mathrm{kg\,m^2}$ . The value of $x$ is .
We corrected a printing error in the original paper
Source printed “ $\dfrac{x}{2}ML^2$ ” (which gives $x = 17/6$ ); corrected to the intended “ $\dfrac{x}{12}ML^2$ ” ( $I = 17ML^2/12$ , source key 17).
PhysicsJEE Main 22 Jan 2026, Shift 1·Q1·MCQ·Easy–moderate
Open
A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is $\mathrm{kg.m^2}$ .
1. (1)0.36
2. (2)0.72
3. (3)0.18
4. (4)0.63
PhysicsJEE Main 22 Jan 2026, Shift 1·Q24·Numerical·Easy–moderate
Open
A circular disc has radius $R_1$ and thickness $T_1$ . Another circular disc made of the same material has radius $R_2$ and thickness $T_2$ . If the moments of inertia of both discs are same and $\dfrac{R_1}{R_2} = 2$ then $\dfrac{T_1}{T_2} = \dfrac{1}{\alpha}$ . The value of $\alpha$ is .
We corrected a printing error in the original paper
Source printed “the moment of inertia of both discs are same”.
PhysicsJEE Main 23 Jan 2026, Shift 1·Q8·MCQ·Moderate
Open
The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length L $(R < L)$ about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M):
1. (1) $\dfrac38 MR^2 + \dfrac{7}{12}ML^2$
2. (2) $\dfrac34 MR^2 + \dfrac16 ML^2$
3. (3) $\dfrac34 MR^2 + \dfrac{7}{12}ML^2$
4. (4) $\dfrac38 MR^2 + \dfrac16 ML^2$
PhysicsJEE Main 23 Jan 2026, Shift 2·Q24·Numerical·Moderate
Open
Suppose there is a uniform circular disc of mass $M$ kg and radius $r$ m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by $\dfrac{x}{256}Mr^2$ . The value of $x$ is .
PhysicsJEE Main 24 Jan 2026, Shift 2·Q24·Numerical·Easy–moderate
Open
A uniform solid cylinder of length $L$ and radius $R$ has moment of inertia about its axis equal to $I_1$ . A small concentric cylinder of length $L/2$ and radius $R/3$ carved from this cylinder has moment of inertia about its axis equal to $I_2$ . The ratio $I_1/I_2$ is .
We corrected a printing error in the original paper
Source printed “A small co-centric cylinder” and “about its axis equals to $I_2$ ”.
PhysicsJEE Main 28 Jan 2026, Shift 1·Q23·Numerical·Easy–moderate
Open
A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is $\sqrt{n}$ cm. The value of $n$ is
PhysicsJEE Main 2 Apr 2026, Shift 2·Q25·Numerical·Easy–moderate
Open
Moment of inertia about an axis AB for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass of 10 kg and radius R about an axis parallel to AB axis with separation of 3 m as shown in figure below. The value of R is given as $\sqrt{\dfrac{\alpha}{2}}$ . The value of $\alpha$ is .
PhysicsJEE Main 4 Apr 2026, Shift 1·Q5·MCQ·Moderate
Open
A solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The smaller part having mass $M/8$ is converted into a sphere of radius $r$ and the larger part is converted into a circular disc of thickness $t$ and radius $2R$ . If $I_1$ is moment of inertia of a sphere having radius $r$ about an axis through its centre and $I_2$ is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia $I_2/I_1 =$ .
1. (1)35
2. (2)70
3. (3)140
4. (4)210
We corrected a printing error in the original paper
Source printed “mas”.

Rotational kinematics and torque

PhysicsJEE Main 21 Jan 2026, Shift 2·Q6·MCQ·Easy–moderate
Open
Two cars A and B each of mass $10^{3}$ kg are moving on parallel tracks separated by a distance of 10 m, in same direction with speeds 72 km/h and 36 km/h. The magnitude of angular momentum of car A with respect to car B is J.s.
1. (1) $3.6\times10^{5}$
2. (2) $10^{5}$
3. (3) $3\times10^{5}$
4. (4) $2\times10^{5}$
PhysicsJEE Main 22 Jan 2026, Shift 2·Q4·MCQ·Moderate
Open
A uniform bar of length 12 cm and mass 20 $m$ lies on a smooth horizontal table. Two point masses m and 2 $m$ are moving in opposite directions with same speed of v and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency $\omega$ . The ratio of v and $\omega$ (in cm) is :
1. (1)33
2. (2) $2\sqrt{88}$
3. (3)66
4. (4)32
We corrected a printing error in the original paper
Source printed “The ratio of v and $\omega$ is” with unitless options ( $v/\omega$ is a length; 33 cm).
PhysicsJEE Main 28 Jan 2026, Shift 2·Q12·MCQ·Easy–moderate
Open
When the position vector $\vec r = x\hat i + y\hat j + z\hat k$ changes sign as $-\vec r$ , which one of the following vectors will not flip under sign change?
1. (1)Linear momentum
2. (2)Velocity
3. (3)Acceleration
4. (4)Angular momentum
We corrected a printing error in the original paper
Source printed “which one of the following vector”.
PhysicsJEE Main 2 Apr 2026, Shift 1·Q6·MCQ·Easy–moderate
Open
A particle is rotating in a circular path and at any instant its motion can be described as $\theta = \dfrac{5t^4}{40} - \dfrac{t^3}{3}$ . The angular acceleration of the particle after 10 seconds is $\mathrm{rad/s^2}$ .
1. (1)150
2. (2)120
3. (3)130
4. (4)170
PhysicsJEE Main 5 Apr 2026, Shift 2·Q5·MCQ·Easy–moderate
Open
A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $\theta_1$ and in the next 2 s it rotates through an angle $\theta_2$ . The ratio $\dfrac{\theta_2}{\theta_1}$ is.
1. (1)6
2. (2)3
3. (3)4
4. (4) $\dfrac13$