Mock Test 1 — Rotational Motion

The MI of a uniform rod of mass $M$ and length $L$ about an axis perpendicular through its centre is:

A solid cylinder rolls without slipping with KE $30$ J. Its translational KE is:

The angular momentum of a particle moving along a straight line with constant velocity, about a point not on the line:

The radius of gyration of a uniform rod about a perpendicular axis through its end is:

A wheel of MI $4$ kg·m² is subjected to a torque of $10$ N·m for $4$ s. The change in angular velocity:

The angular momentum of a system is conserved when:

A solid sphere and a hollow sphere of same mass and radius roll without slipping. Ratio of their KE for same $v_{cm}$:

The MI of a thin ring about a diameter is:

Two particles of equal masses $m$ are at $(0, 0)$ and $(a, 0)$. Position of CM:

A pulley of MI $2$ kg·m² and radius $0.1$ m has a string with a $1$ kg mass attached. Acceleration of the mass ($g = 10$):

A wheel rotating at $300$ rpm slows to $60$ rpm uniformly in $20$ s. Angular deceleration in rad/s² (rounded):

A solid sphere rolls down an incline of $\sin\theta = 0.7$. Acceleration (m/s², $g = 10$, rounded):

A disc of mass $1$ kg, radius $0.2$ m rotates at $10$ rad/s. Its angular momentum (in $10^{-2}$ kg·m²/s units):

Assertion (A): When a planet revolves around the sun, its angular momentum is conserved. Reason (R): The gravitational force on the planet acts along the radial direction; hence torque is zero.

Assertion (A): Rolling friction is less than sliding friction. Reason (R): A body rolling on a surface has its contact point instantaneously at rest.