A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed $$\omega$$, as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v, with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains $$\omega$$ throughout. The magnitude of the torque (|$$\tau$$|) about O, as a function of time is best represented by which plot ?
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant $$k$$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $${\overrightarrow V _0} = {V_0}\widehat i$$. the coefficient of friction is $$\mu$$.
The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is :
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant $$k$$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $${\overrightarrow V _0} = {V_0}\widehat i$$. the coefficient of friction is $$\mu$$.
The centre of mass of the disk undergoes simple harmonic motion with angular frequency $$\omega$$ equal to:
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant $$k$$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $${\overrightarrow V _0} = {V_0}\widehat i$$. the coefficient of friction is $$\mu$$.
The maximum value of V$$_0$$ for which the disk will roll without slipping is: