JEE Main 2025 January Physics: Rotational Motion – Previous Year Questions

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :

The center of mass of a thin rectangular plate (fig - x) with sides of length $a$ and $b$, whose mass per unit area ($\sigma$) varies as $\sigma=\frac{\sigma_0 x}{ab}$ (where $\sigma_0$ is a constant), would be .

A uniform circular disc of radius 'R' and mass 'M' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2 is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is $n$ times higher than the moment of inertia of the given ring. Here, $n=$ . Consider all the bodies have equal masses.

The position vectors of two 1 kg particles, (A) and (B), are given by $\vec r_A=(\alpha_1t^2\hat i+\alpha_2t\hat j+\alpha_3t\hat k)$ m and $\vec r_B=(\beta_1t\hat i+\beta_2t^2\hat j+\beta_3t\hat k)$ m, respectively; ($\alpha_1=1$ m/s$^2$, $\alpha_2=3n$ m/s, $\alpha_3=2$ m/s, $\beta_1=2$ m/s, $\beta_2=-1$ m/s$^2$, $\beta_3=4p$ m/s), where $t$ is time, $n$ and $p$ are constants. At $t=1$ s, $|\vec v_A|=|\vec v_B|$ and velocities $\vec v_A$ and $\vec v_B$ of the particles are orthogonal to each other. At $t=1$ s, the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is $\sqrt{L}$ kg m$^2$ s$^{-1}$. The value of $L$ is .

The torque due to the force $(2\hat i+\hat j+2\hat k)$ about the origin, acting on a particle whose position vector is $(\hat i+\hat j+\hat k)$, would be

A circular disk of radius $R$ meter and mass $M$ kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that $\theta(t)=5t^2-8t$, where $\theta(t)$ is the angular position of the rotating disc as a function of time $t$. How much power is delivered by the applied torque, when $t=2$ s ?

An object of mass 'm' is projected from origin in a vertical $xy$ plane at an angle $45^\circ$ with the $x$-axis with an initial velocity $v_0$. The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [$g$ is acceleration due to gravity]

Two iron solid discs of negligible thickness have radii $R_1$ and $R_2$ and moment of intertia $I_1$ and $I_2$, respectively. For $R_2=2R_1$, the ratio of $I_1$ and $I_2$ would be $1/x$, where $x=$ .

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of $\vec F=\hat i-\hat j+\hat k$ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is .

A solid sphere of mass 'm' and radius 'r' is allowed to roll without slipping from the highest point of an inclined plane of length 'L' and makes an angle $30^\circ$ with the horizontal. The speed of the particle at the bottom of the plane is $v_1$. If the angle of inclination is increased to $45^\circ$ while keeping L constant. Then the new speed of the sphere at the bottom of the plane is $v_2$. The ratio $v_1^2:v_2^2$ is

A uniform solid cylinder of mass 'm' and radius 'r' rolls along an inclined rough plane of inclination $45^\circ$. If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_1$ and $t_2$, respectively, then